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J. L. Brown, Jr. A Generalization of Semi-Completeness
for Integer Sequences . . . . . . . . . 3--15
Paul F. Byrd Expansion of Analytic Functions in
Polynomials Associated with Fibonacci
Numbers . . . . . . . . . . . . . . . . 16--27
Anonymous Problem Department . . . . . . . . . . . 28--29
H. W. Gould Operational Recurrences Involving
Fibonacci Numbers . . . . . . . . . . . 30--33
Brother U. Alfred Additional Factors of the Fibonacci and
Lucas Series . . . . . . . . . . . . . . 34--42
Brother U. Alfred On the Form of Primitive Factors of
Fibonacci Numbers . . . . . . . . . . . 43--45
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 46--48
Dmitri Thoro Beginners' Corner . . . . . . . . . . . 49--52
S. L. Basin The Fibonacci Sequence As It Appears in
Nature . . . . . . . . . . . . . . . . . 53--56
Brother U. Alfred Exploring Fibonacci Numbers . . . . . . 57--63
Dmitri Thoro Solutions, Beginner's Corner . . . . . . 64
S. L. Basin and
Verner E. Hoggatt, Jr. A Primer on the Fibonacci Sequence, Part
I . . . . . . . . . . . . . . . . . . . 65--72
S. L. Basin Elementary Problems and Solutions . . . 73
Anonymous Cover Page . . . . . . . . . . . . . . . ??
H. W. Gould Generating Functions for Products of
Powers of Fibonacci Numbers . . . . . . 1--16
L. Carlitz A Fibonacci Array . . . . . . . . . . . 17--28
D. W. Robinson The Fibonacci Matrix Modulo $m$ . . . . 29--36
John Vinson The Relation of the Period Modulo $m$ to
the Rank of Apparition of $m$ in the
Fibonacci Sequence . . . . . . . . . . . 37--46
Marjorie Bicknell and
Verner E. Hoggatt, Jr. Fibonacci Matrices and Lambda Functions 47--52
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 53--55
Anonymous Generating Fibonacci Series on a Desk
Calculator . . . . . . . . . . . . . . . 56
Dmitri Thoro Beginners' Corner . . . . . . . . . . . 57--59
Maxey Brooke Letter to the Editor: Fibonacci Formulas 60
S. L. Basin and
Verner E. Hoggatt, Jr. A Primer on the Fibonacci Sequence, Part
II . . . . . . . . . . . . . . . . . . . 61--68
James A. Jeske Linear Recurrence Relations, Part I . . 69--73
Anonymous Problem Department . . . . . . . . . . . 74
I. Dale Ruggles Some Fibonacci Results Using
Fibonacci-Type Sequences . . . . . . . . 75--79
Dmitri Thoro Hints to Beginner's Corner Problems . . 80
Brother U. Alfred Exploring Recurrent Sequences . . . . . 81--83
Stephen P. Geller A Computer Investigation of a Property
of the Fibonacci Sequence . . . . . . . 84
S. L. Basin Elementary Problems and Solutions . . . 85
V. E. Hoggatt, Jr. and
S. L. Basin Representations by Complete Sequences
--- Part I (Fibonacci) . . . . . . . . . 1--14
Dov Jarden On the Greatest Primitive Divisors of
Fibonacci and Lucas Numbers With
Prime-Power Subscripts . . . . . . . . . 15--20
Joseph A. Raab A Generalization of the Connection
Between the Fibonacci Sequence and
Pascal's Triangle . . . . . . . . . . . 21--31
Anonymous Obituary for Morgan Ward . . . . . . . . 32
Brother U. Alfred Periodic Properties of Fibonacci
Summations . . . . . . . . . . . . . . . 33--41
Charles Ziegenfus Letter to the Editor: Twin Primes . . . 42
A. P. Hillman and
M. T. Stroot and
R. M. Grassl Fibonacci Numbers and Zigzag Hasse
Diagrams . . . . . . . . . . . . . . . . 43--45
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 46--52
Dmitri Thoro Beginners' Corner . . . . . . . . . . . 53--59
Brother U. Alfred Exploring Fibonacci Polygons . . . . . . 60
I. D. Ruggles and
Verner E. Hoggatt, Jr. A Primer on the Fibonacci Sequence, Part
III . . . . . . . . . . . . . . . . . . 61--65
J. A. H. Hunter Triangle Inscribed in Rectangle . . . . 66
Ken Siler Fibonacci Summations . . . . . . . . . . 67--70
Mark Feinberg Fibonacci--Tribonacci . . . . . . . . . 71--74
S. L. Basin Elementary Problems and Solutions . . . 75
R. G. Buschman Fibonacci Numbers, Chebyshev
Polynomials, Generalizations and
Difference Equations . . . . . . . . . . 1--7
Anonymous History of the Fibonacci Quarterly . . . 8
Michael J. Whinihan Fibonacci Nim . . . . . . . . . . . . . 9--14
Charles King Leonardo Fibonacci . . . . . . . . . . . 15--20
Dov Jarden On the Periodicity of the Last Digits of
the Fibonacci Numbers . . . . . . . . . 21--22
Charles R. Wall Some Remarks on Carlitz's Fibonacci
Array . . . . . . . . . . . . . . . . . 23--29
Dmitri Thoro Reciprocals of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 30
H. W. Gould Fibonacci Exponentials and
Generalizations of Hermite Polynomials 31--34
James A. Jeske Linear Recurrence Relations --- Part III 35--40
A. F. Horadam Further Appearance of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 41--42
Brother U. Alfred On the Ordering of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 43--46
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 47--52
Brother U. Alfred Dying Rabbit Problem Revived . . . . . . 53--56
Sister Mary de Sales McNabb Phyllotaxis . . . . . . . . . . . . . . 57--60
J. Wlodarski The ``Golden Ratio'' and the Fibonacci
Numbers in the World of Atoms . . . . . 61--64
I. D. Bruggles and
V. E. Hoggatt, Jr. A Primer on the Fibonacci Sequence, Part
IV . . . . . . . . . . . . . . . . . . . 65--71
Brother U. Alfred Exploring the Fibonacci Representation
of Integers . . . . . . . . . . . . . . 72
S. L. Basin Elementary Problems and Solutions . . . 73
Anonymous Index to Volume I . . . . . . . . . . . ??
R. L. Graham A Property of Fibonacci Numbers . . . . 1--10
Brother U. Alfred On Square Lucas Numbers . . . . . . . . 11--12
Robert E. Greenwood Lattice Paths and Fibonacci Numbers . . 13--14
L. Carlitz A Note on Fibonacci Numbers . . . . . . 15--28
Verner E. Hoggatt, Jr. and
Marjorie Bicknell Some New Fibonacci Identities . . . . . 29--31
Anonymous Corrections . . . . . . . . . . . . . . 32
Brother U. Alfred Primes Which Are Factors Of All
Fibonacci Sequences . . . . . . . . . . 33--38
J. H. Jordan A Fibonacci Test For Convergence . . . . 39--41
Brother U. Alfred Exploring Fibonacci Residues . . . . . . 42
Donald Knuth Transcendental Numbers Based On The
Fibonacci Sequence . . . . . . . . . . . 43--44
Dov Jarden Strengthened Inequalities For Fibonacci
And Lucas Numbers . . . . . . . . . . . 45--48
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 49--52
Dmitri Thoro Beginners' Corner . . . . . . . . . . . 53--56
Glen Michael A New Proof For An Old Property . . . . 57--58
Verner E. Hoggatt, Jr. and
I. D. Bruggles A Primer on the Fibonacci Sequence, Part
V . . . . . . . . . . . . . . . . . . . 59--66
Francis D. Parker On the General Term of a Recursive
Sequence . . . . . . . . . . . . . . . . 67--71
A. P. Hillman Elementary Problems and Solutions . . . 72--80
Brother U. Alfred Some Determinants Involving Powers of
Fibonacci Numbers . . . . . . . . . . . 81--92
Terrence A. Brennan Fibonacci Powers and Pascal's Triangle
in a Matrix . . . . . . . . . . . . . . 93--103
H. E. Huntley Fibonacci Geometry . . . . . . . . . . . 104
David Zeitlin On Summation Formulas for Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 105--107
John H. E. Cohn Letter to the Editor . . . . . . . . . . 108
John H. E. Cohn Square Fibonacci Numbers, Etc. . . . . . 109--113
Phil Lafer Exploring the Fibonacci Representation
of Integers . . . . . . . . . . . . . . 114
Daniel Fielder Partition Enumeration by Means of
Simpler Partitions . . . . . . . . . . . 115--117
Anonymous Corrections . . . . . . . . . . . . . . 118
S. L. Basin A Note on Waring's Formula for Sums of
Like Powers of Roots . . . . . . . . . . 119--121
Anonymous Omissions . . . . . . . . . . . . . . . 122
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 123--134
Dmitri Thoro Beginners' Corner . . . . . . . . . . . 135--137
Brother U. Alfred Exploring Fibonacci Numbers with a
Calculator . . . . . . . . . . . . . . . 138
Joseph Mandelson Amateur Interests in the Fibonacci
Series --- Prime Numbers . . . . . . . . 139--144
A. P. Hillman and
G. L. Alexanderson A Motivation for Continued Fractions . . 145--148
Maxey Brooke Fibonacci Numbers: Their History Through
1900 . . . . . . . . . . . . . . . . . . 149--153
A. P. Hillman Elementary Problems and Solutions . . . 154--160
Colonel R. S. Beard Fibonacci Drawing Board . . . . . . . . 161--162
J. L. Brown, Jr. Zeckendorf's Theorem and Some
Applications . . . . . . . . . . . . . . 163--168
L. T. Oliver and
D. J. Wilde Symmetric Sequential Minimax Search for
a Maximum . . . . . . . . . . . . . . . 169--175
Verner E. Hoggatt, Jr. Fibonacci Numbers from a Differential
Equation . . . . . . . . . . . . . . . . 176
T. A. Brennan Fibonacci Powers and Pascal's Triangle
in a Matrix --- Part II . . . . . . . . 177--183
H. E. Huntley The Golden Cuboid . . . . . . . . . . . 184
L. Carlitz A Partial Difference Equation Related to
the Fibonacci Numbers . . . . . . . . . 185--196
J. A. Jeske Linear Recurrence Relations --- Part III 197--202
H. W. Gould Associativity and the Golden Section . . 203
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 204--209
Brother U. Alfred A Digit Muses \ldots . . . . . . . . . . 210
R. L. Heimer Further Comments on the Periodicity of
the Digits of the Fibonacci Sequence . . 211--214
B. B. Sharpe The Vanishing Square . . . . . . . . . . 215
Brother U. Alfred Exploring Fibonacci Magic Squares . . . 216
J. H. Halton On Fibonacci Residues . . . . . . . . . 217
David M. Bloom Corrected Factorizations of Fibonacci
Numbers . . . . . . . . . . . . . . . . 218
H. Norden Proportions in Music . . . . . . . . . . 219
J. Brillhart Remarks on a Second Order Recurring
Sequence . . . . . . . . . . . . . . . . 220--222
M. Feinberg New Slants . . . . . . . . . . . . . . . 223--227
W. W. Horner Fibonacci and Pascal . . . . . . . . . . 228
E. Lehmer On the Infinitude of Fibonacci
Pseudo-Primes . . . . . . . . . . . . . 229
J. A. H. Hunter Two Very Special Numbers . . . . . . . . 230
A. P. Hillman Elementary Problems and Solutions . . . 231--240
H. W. Gould Binomial Coefficients, the Bracket
Function, and Composition with
Relatively Prime Summands . . . . . . . 241--259
B. G. Baumgart Letter to the Editor . . . . . . . . . . 260
Verner E. Hoggatt, Jr. and
Marjorie Bicknell Fourth Power Fibonacci Identities from
Pascal's Triangle . . . . . . . . . . . 261--266
Peter Hagis, Jr. An Analytic Proof of the Formula for $
F_n $ . . . . . . . . . . . . . . . . . 267--268
Brother U. Alfred Continued Fractions and Fibonacci and
Lucas Ratios . . . . . . . . . . . . . . 269--276
V. C. Harris and
Carolyn C. Styles A Generalization of Fibonacci Numbers 277--289
N. A. Draim Expansion of Pi in Terms of an Infinite
Continued Fraction with Predictable
Terms . . . . . . . . . . . . . . . . . 290
Dmitri Thoro An Application of Unimodular
Transformations . . . . . . . . . . . . 291--295
Roseanna F. Torretto and
J. Allen Fuchs Generalized Binomial Coefficients . . . 296--302
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 303--309
Richard Brian The Problem of the Little Old Lady
Trying to Cross the Busy Street or
Fibonacci Gained and Fibonacci Relost 310--313
Ben L. Swensen Application of Fibonacci Numbers to
Solutions of Systems of Linear Equations 314--316
B. B. Sharpe A Fibonacci --- Prime Number Relation 317
Brother U. Alfred Exploring Geometric--Algebraic Fibonacci
Patterns . . . . . . . . . . . . . . . . 318--319
Albert J. Faulconbridge Fibonacci Summation Economics Part I . . 320--322
A. P. Hillman Elementary Problems and Solutions . . . 323--330
Anonymous Volume Index . . . . . . . . . . . . . . 331
J. L. Brown, Jr. A New Characterization of the Fibonacci
Numbers . . . . . . . . . . . . . . . . 1--8
David A. Klarner Some Results Concerning Polyominoes . . 9--20
H. H. Ferns On the Representation of Integers as
Sums of Distinct Fibonacci Numbers . . . 21--30
John H. Halton On a General Fibonacci Identity . . . . 31--43
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 44--52
Brother U. Alfred Math Morals (a Limerick) . . . . . . . . 53
Sheryl B. Tadlock Products of Odds . . . . . . . . . . . . 54--56
C. B. A. Peck Exploring Scalene Fibonacci Polygons . . 57--58
Brother U. Alfred Note on Third Order Determinants . . . . 59--60
Jeremy C. Pond and
Donald F. Howells More on Fibonacci Nim . . . . . . . . . 61--62
Benjamin Sharpe On Sums $ F_x^2 \pm F_y^2 $ . . . . . . 63
E. J. Karchmar Phyllotaxis . . . . . . . . . . . . . . 64--65
Anonymous Corrections . . . . . . . . . . . . . . 66
Marjorie Bicknell Fibonacci Fantasy: The Square Root of
the $Q$ Matrix . . . . . . . . . . . . . 67--70
P. Naor Letter to the Editor . . . . . . . . . . 71--73
A. P. Hillman Elementary Problems and Solutions . . . 74--80
L. Carlitz The Characteristic Polynomial of a
Certain Matrix of Binomial Coefficients 81--89
Charles W. Trigg A Recursive Operation on Two-Digit
Integers . . . . . . . . . . . . . . . . 90
V. E. Hoggatt, Jr. and
A. P. Hillman The Characteristic Polynomial of the
Generalized Shift Matrix . . . . . . . . 91--94
Selmo Tauber Summation Formulae for Multinomial
Coefficients . . . . . . . . . . . . . . 95--100
Paul F. Byrd Expansion of Analytic Functions in Terms
Involving Lucas Numbers or Similar
Number Sequences . . . . . . . . . . . . 101--113
Anonymous Correction . . . . . . . . . . . . . . . 114
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 115--128
Brother U. Alfred Seeking the Lost Gold Mine or Exploring
for Fibonacci Factorizations . . . . . . 129--130
Henry Winthrop Time Generated Compositions Yield
Fibonacci Numbers . . . . . . . . . . . 131--134
Marvin H. Holt Mystery Puzzler and Phi . . . . . . . . 135--138
Joseph Arkin Ladder Network Analysis Using
Polynomials . . . . . . . . . . . . . . 139--142
Douglas R. Stocks, Jr. Concerning Lattice Paths and Fibonacci
Numbers . . . . . . . . . . . . . . . . 143--145
John L. Brown, Jr. Reply to Exploring Fibonacci Magic
Squares . . . . . . . . . . . . . . . . 146
Eric Halsey The Fibonacci Number $ {F}_u $ where $u$
is not an Integer . . . . . . . . . . . 147--152
A. P. Hillman Elementary Problems and Solutions . . . 153--159
Anonymous Acknowledgments and Corrections . . . . 160
A. F. Horadam Basic Properties of a Certain
Generalized Sequence of Numbers . . . . 161--176
H. W. Gould Non-Fibonacci Numbers . . . . . . . . . 177--183
Anonymous Corrections . . . . . . . . . . . . . . 184
Dmitri Thoro Two Fibonacci Conjectures . . . . . . . 184--186
Robert B. Ely III Fibonaccious Factors . . . . . . . . . . 187--198
R. G. Buschman A Generating Function for Fibonacci
Numbers . . . . . . . . . . . . . . . . 199--200
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 201--207
J. Wlodarski The Fibonacci Numbers and the ``Magic''
Numbers . . . . . . . . . . . . . . . . 208
D. G. Mead An Elementary Method of Summation . . . 209--213
V. C. Harris On Identities Involving Fibonacci
Numbers . . . . . . . . . . . . . . . . 214--218
R. P. Kelisky Concerning the Euclidean Algorithm . . . 219--223
Brother U. Alfred A Strip Method of Summing Linear
Fibonacci Expressions . . . . . . . . . 224--226
Marjorie Bicknell and
James Leissner A Near-golden Rectangle and Related
Recursive Series . . . . . . . . . . . . 227--231
L. A. G. Dresel and
D. E. Daykin Factorization of 36 Fibonacci Numbers $
F_n $ with $ n > 100 $ . . . . . . . . . 232
Eric Halsey Letter to the Editor . . . . . . . . . . 233
Henry Winthrop Comments on ``Time Generated,
Compositions Yield Fibonacci Numbers'' 234
A. P. Hillman Elementary Problems and Solutions . . . 235--240
David Zeitlin Power Identities for Sequences Defined
by $ W_{n + 2} = d W_{n + 1} - d W_n $ 241--256
Anonymous Omission . . . . . . . . . . . . . . . . 257
H. W. Gould A Variant of Pascal's Triangle . . . . . 257--271
I. I. Kolodner On a Generating Function Associated with
Generalized Fibonacci Sequences . . . . 272--278
W. D. Skees A Permutative Property of Certain
Multiples of the Natural Numbers . . . . 279--291
D. A. Lind On a Class of Nonlinear Binomial Sums 292--298
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 299--303
Clyde A. Bridger and
Marjorie Bicknell Continued Fraction Convergents as a
Source of Fibonacci and Lucas Identities 304--308
Albert J. Faulconbridge Fibonacci Summation Economics Part II 309--314
J. H. Jordan Gaussian Fibonacci and Lucas Numbers . . 315--318
Brother U. Alfred Exploring Generalized Fibonacci--Lucas
Relations . . . . . . . . . . . . . . . 319--320
John H. Halton A Note on Fibonacci Subsequences . . . . 321--322
A. P. Hillman Elementary Problems and Solutions . . . 323--329
Betty Naysmith Op Art . . . . . . . . . . . . . . . . . 330
Anonymous Volume Index . . . . . . . . . . . . . . 331
John C. Holladay Some Convergent Recursive Sequences,
Homeomorphic Identities, and Inductively
Defined Complementary Sequences . . . . 1--36
Raymond E. Whitney Extensions of Recurrence Relations . . . 37--42
L. Carlitz Some Orthogonal Polynomials Related to
Fibonacci Numbers . . . . . . . . . . . 43--48
J. C. Ahuja and
S. W. Nash A Note on Orthogonal Polynomials . . . . 49--55
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 56--58
H. W. Gould A Fibonacci Crossword Puzzle . . . . . . 59--62
Edgar I. Emerson On the Integer Solution of the Equation
$ 5 x^2 + 6 x + 1 = y^2 $ and Some
Related Observations . . . . . . . . . . 63--69
R. S. Beard Star Geometry . . . . . . . . . . . . . 70--72
M. N. S. Swamy Properties of the Polynomials Defined by
Morgan--Voyce . . . . . . . . . . . . . 73--81
J. A. H. Hunter Perfect Number ``Endings'' . . . . . . . 82
Lenard Weinstein A Divisibility Property of Fibonacci
Numbers . . . . . . . . . . . . . . . . 83--84
Enrico T. Federighi and
Ronald G. Roll A Letter to the Editor . . . . . . . . . 85--87
Lenard Weinstein Letter to the Editor . . . . . . . . . . 88
Gerard R. Deily A Logarithmic Formula for Fibonacci
Numbers . . . . . . . . . . . . . . . . 89
A. P. Hillman Elementary Problems and Solutions . . . 90--96
F. D. Cashwell and
C. J. Everett Fibonacci Spaces . . . . . . . . . . . . 97--115
J. W. Layman Relatively Prime Sequence Solutions of
Non-linear Difference Equations . . . . 116
Donald E. Knuth An Almost Linear Recurrence . . . . . . 117--128
L. Carlitz Some Determinants Containing Powers of
Fibonacci Numbers . . . . . . . . . . . 129--134
E. Lehmer On the Quadratic Character of the
Fibonacci Root . . . . . . . . . . . . . 135--138
C. C. Styles On Evaluating Certain Coefficients . . . 139--147
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 148--149
H. W. Gould A Fibonacci Crossword Puzzle . . . . . . 150
G. R. Deily Terminal Digit Coincidences Between
Fibonacci Numbers and Their Indices . . 151--156
M. Berg Phi, the Golden Ratio (to 4599 Decimal
Places), and Fibonacci Numbers . . . . . 157--162
R. S. Beard Powers of the Golden Section . . . . . . 163--167
W. W. Horner Fibonacci and Euclid . . . . . . . . . . 168--169
N. A. Draim and
Marjorie Bicknell Sums of $n$-th Powers of Roots of a
Given Quadratic Equation . . . . . . . . 170--178
D. A. Klarner Determinants Involving $K$ th Powers
from Second Order Sequences . . . . . . 179--183
F. S. Gillespie and
W. R. Utz A Generalized Langford Problem . . . . . 184--186
B. L. Foster A Lower Bound for Maximum Zero-one
Determinants . . . . . . . . . . . . . . 187--189
A. P. Hillman Elementary Problems and Solutions . . . 190--192
J. A. Fridy Gerneralized Bases for the Real Numbers 193--200
Anonymous Announcement . . . . . . . . . . . . . . 201
W. Jentsch On a Partial Difference Equation of L.
Carlitz . . . . . . . . . . . . . . . . 202--207
Brother Alfred Brousseau Book Review: \booktitleRecurring
Sequences, by Dov Jarden . . . . . . . . 208
Daniel C. Fielder Enumeration of Partitions Subject to
Limitations on Size of Members . . . . . 209--215
Anonymous Announcement . . . . . . . . . . . . . . 216
John H. Halton On the Divisibility Properties of
Fibonacci Numbers . . . . . . . . . . . 217--240
V. C. Harris and
Carolyn C. Styles Generalized Fibonacci Sequences
Associated with a Generalized Pascal
Triangle . . . . . . . . . . . . . . . . 241--248
John C. Holladay Corrigendum for ``Some Convergent
Recursive Sequences, Homomorphic
Identities, and Inductively Defined
Complementary Sequences'' . . . . . . . 249--250
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 251--258
Curtis McKnight and
Dean Priest A Singular Fibonacci Matrix and its
Related Lambda Function . . . . . . . . 259--261
Brother U. Alfred Exploring Special Fibonacci Relations 262--263
Brother U. Alfred \booktitleAlgebra Through Problem
Solving --- Book Review . . . . . . . . 264
Mordecai Avriel and
Douglass J. Wilde Optimality Proof for the Symmetric
Fibonacci Search Technique . . . . . . . 265--269
David E. Ferguson An Expression for Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 270--272
J. A. H. Hunter Fibonacci Again . . . . . . . . . . . . 273
V. E. Hoggatt, Jr. and
D. A. Lind A Power Identity for Second-order
Recurrent Sequences . . . . . . . . . . 274--284
A. P. Hillman Elementary Problems and Solutions . . . 285--288
David A. Klarner Representation of $N$ as a Sum of
Distinct Elements from Special Sequences 289--306
Eugene E. Kohlbecker On a Generalization of Multinomial
Coefficients for Fibonacci Sequences . . 307--312
Robert P. Backstrom On the Determination of the Zeros of the
Fibonacci Sequence . . . . . . . . . . . 313--322
L. Carlitz Some Binomial Coefficient Identities . . 323--331
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 332--338
M. Dunton and
R. E. Grimm Fibonacci on Egyptian Fractions . . . . 339--353
Donald E. Knuth Correction: ``An almost linear
recurrence'' . . . . . . . . . . . . . . 354--354
John Wessner Binomial Sums of Fibonacci Powers . . . 355--358
Joseph Arkin A Note on a Theorem of Jacobi . . . . . 359--362
Raymond E. Whitney Composition of Recursive Formulae . . . 363--366
R. L. Duncan Note on the Euclidean Algorithm . . . . 367--368
M. N. S. Swamy More Fibonacci Identities . . . . . . . 369--372
A. P. Hillman Elementary Problems and Solutions . . . 373--378
Anonymous Volume Index . . . . . . . . . . . . . . 379
David Zeitlin On Summation Formulas and Identities for
Fibonacci Numbers . . . . . . . . . . . 1--43
D. A. Lind The $Q$ Matrix as a Counterexample in
Group Theory . . . . . . . . . . . . . . 44
George Ledin, Jr. On a Certain Kind of Fibonacci Sums . . 45--58
C. A. Church, Jr. and
H. W. Gould Lattice Point Solution of the
Generalized Problem of Terquem and an
Extension of Fibonacci Numbers . . . . . 59--68
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 69--80
Douglas R. Stocks, Jr. Relations Involving Lattice Paths and
Certain Sequences of Integers . . . . . 81--86
Dewey C. Duncan Chains of Equivalent Fibonacci-Wise
Triangle . . . . . . . . . . . . . . . . 87--88
D. A. Lind Iterated Fibonacci and Lucas Subscripts 89--90
Brother Alfred Brousseau Summation of $ \sum_{k = 1}^n k^m F_{k +
r} $ Finite Difference Approach . . . . 91--98
G. F. Feeman On Ratios of Fibonacci and Lucas Numbers 99--106
A. P. Hillman Elementary Problems and Solutions . . . 107--112
C. T. Long and
J. H. Jordan A Limited Arithmetic on Simple Continued
Fractions . . . . . . . . . . . . . . . 113--128
Gary G. Ford Recurrence Relations for Sequences like
$ F_{F_n} $ . . . . . . . . . . . . . . 129--136
R. L. Duncan An Application of Uniform Distributions
to the Fibonacci Numbers . . . . . . . . 137--140
V. E. Hoggatt, Jr. and
D. A. Lind The Heights of Fibonacci Polynomials and
an Associated Function . . . . . . . . . 141--152
J. L. Brown, Jr. On Lamé's Theorem . . . . . . . . . . . . 153--160
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 161
Anonymous Corrections . . . . . . . . . . . . . . 162--168
Brother Alfred Brousseau Editorial . . . . . . . . . . . . . . . 169--170
Brother Alfred Brousseau A Fibonacci Generalization . . . . . . . 171--174
Robert Pruitt Fibonacci and Lucas Numbers in the
Sequence of Golden Numbers . . . . . . . 175--178
John D. Neff A Markov Limit Process Involving
Fibonacci Numbers . . . . . . . . . . . 179--182
D. A. Lind Extended Computations of Terminal Digit
Coincidences . . . . . . . . . . . . . . 183--184
H. B. Henning Pythagorean Triangles and Related
Concepts . . . . . . . . . . . . . . . . 185--192
J. Wlodarski Achieving the ``Golden Ratio'' by
Grouping the ``Elementary'' Principle 193--194
Kathleen Weland Some Rabbit Production Results Involving
Fibonacci Numbers . . . . . . . . . . . 195--200
A. P. Hillman Elementary Problems and Solutions . . . 201--207
Brother Alfred Brousseau 1967 as the Sum of Squares . . . . . . . 208
Marcellus E. Waddill and
Louis Sacks Another Generalized Fibonacci Sequence 209--222
S. G. Mohanty Restricted Compositions . . . . . . . . 223--234
D. P. Roselle Enumeration of Certain Triangular Arrays 235--246
H. W. Gould Note on a Combinatorial Identity in the
Theory of Bi-Colored Graphs . . . . . . 247--250
Verner E. Hoggatt, Jr. Advanced Problems and Solutions . . . . 251--258
Ivan Flores Direct Calculation of $k$-Generalized
Fibonacci Numbers . . . . . . . . . . . 259--266
N. A. Draim and
Marjorie Bicknell Equations Whose Roots as the $n$ th
Powers of the Roots of a Given Cubic
Equation . . . . . . . . . . . . . . . . 267--274
Joseph Mandelson Amateur Interests in the Fibonacci
Series II. Calculation of Fibonacci
Numbers and Sums from the Binomial . . . 275--279
Dov Jarden Existence of Arbitrarily Long Sequences
of Consecutive Members in Arithmetic
Progressions Divisible by Arbitrarily
Many Different Primes . . . . . . . . . 280
Raymond E. Whitney A Property of Linear Recursion Relations 281--285
Dov and
Moshe Jarden Simultaneous Prime and Composite Members
in Two Arithmetic Progressions . . . . . 286
A. P. Hillman Elementary Problems and Solutions . . . 287--293
R. S. Bucknell Fibonacci Numbers and Some Prime
Reciprocals . . . . . . . . . . . . . . 294--297
Laurence Taylor Residues of Fibonacci-Like Sequences . . 298--304
John H. E. Cohn On $m$-tic Residues Modulo $n$ . . . . . 305--318
Daniel C. Fielder Certain Lucas-Like Sequences and Their
Generation by Partitions of Numbers . . 319--324
Daniel C. Fielder Remarks on Two Related Sequences of
Numbers . . . . . . . . . . . . . . . . 325--327
Brother Alfred Brousseau \booktitleRecurring Sequences (Review of
Book by Dov Jarden) . . . . . . . . . . 328
D. E. Daykin and
A. J. W. Hilton Bases for Infinite Intervals of Integers 329--345
Dov Jarden A New Important Formula for Lucas
Numbers . . . . . . . . . . . . . . . . 346
John H. Halton Some Properties Associated with Square
Fibonacci Numbers . . . . . . . . . . . 347--354
Charles W. Trigg Picking away at 1967 . . . . . . . . . . 355
Robert Fray A Generating Function Associated with
the Generalized Stirling Numbers . . . . 356--366
D. E. Daykin and
L. A. G. Dresel Identities for Products of Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 367--369
Charles W. Trigg A Letter to the Editors . . . . . . . . 370
Merritt Elmore Fibonacci Functions . . . . . . . . . . 371--382
V. E. Hoggatt, Jr. Fibonacci Numbers and Generalized
Binomial Coefficients . . . . . . . . . 383--400
H. W. Gould The Bracket Function, $q$-Binomial
Coefficients, and some New Stirling
Number Formulas . . . . . . . . . . . . 401--423
A. F. Horadam Special Properties of the Sequence $
W_n(a, b; p, q) $ . . . . . . . . . . . 424--434
Raymond E. Whitney Advanced Problems and Solutions . . . . 435--443
Brother Alfred Brousseau Recreation Corner --- Population
Explosion . . . . . . . . . . . . . . . 444
V. E. Hoggatt, Jr. and
D. A. Lind A Primer for the Fibonacci Numbers: Part
VI . . . . . . . . . . . . . . . . . . . 445--460
Gary G. Ford A Shift Formula for Recurrence Relations
of Order $m$ . . . . . . . . . . . . . . 461--465
A. P. Hillman Elementary Problems and Solutions . . . 466--471
Charles W. Trigg Getting Primed for 1967 . . . . . . . . 472--473
Charles W. Trigg Curiosa in 1967 . . . . . . . . . . . . 474--476
Charles W. Trigg A Digital Bracelet for 1967 . . . . . . 477--480
Richard L. Heimer A General Fibonacci Function . . . . . . 481--483
J. A. H. Hunter A Result for Heronian Triangles . . . . 484--485
Mark Feinberg A Lucas Triangle . . . . . . . . . . . . 486--490
Anonymous Volume Index . . . . . . . . . . . . . . 491
Francis D. Parker A Fibonacci Function . . . . . . . . . . 1--2
Gene B. Gale Factorization of $ 2 \times 2 $ Integral
Matrices With Determinant $ \pm 1 $ . . 3--20
Anonymous Errata . . . . . . . . . . . . . . . . . 21
S. G. Mohanty On a Partition of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 22--33
J. L. Brown, Jr. A Combinatorial Problem Involving
Fibonacci Numbers . . . . . . . . . . . 34--35
David A. Smith Circularly Generated Abelian Groups . . 36--45
Charles H. King Conjugate Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 46--49
Raymond E. Whitney Advanced Problems and Solutions . . . . 50--57
Brother Alfred Brousseau Recreation Corner --- Solution to
Population Explosion . . . . . . . . . . 58--59
Joseph S. Madachy Recreational Mathematics . . . . . . . . 60--68
Brother Alfred Brousseau On the Trail of the California Pine . . 69--76
Herta T. Freitag A Magic Square Involving Fibonacci
Numbers . . . . . . . . . . . . . . . . 77--80
Brother Alfred Brousseau A Sequence of Power Formulas . . . . . . 81--83
Brother Alfred Brousseau Book Review: \booktitle536 Puzzles and
Curious Problems . . . . . . . . . . . . 84
Col. R. S. Beard The Fibonacci Drawing Board --- Design
of the Great Pyramid of Gizeh . . . . . 85--87
Howard Eves Book Review: \booktitleMathematical
Quickies . . . . . . . . . . . . . . . . 88
A. P. Hillman Elementary Problems and Solutions . . . 89--95
Dov Jarden Formulas for Decomposing $ F_{3n} / F_n
$, $ F_{5n} / F_n $ and $ L_{5n} / L_n $
into a Sum of Difference of Two Squares 96
Jeremy C. Pond Generalized Fibonacci Summations . . . . 97--108
L. R. Shenton Periodicity and Density of Modified
Fibonacci Sequences . . . . . . . . . . 109--116
T. W. Cusick On a Certain Integer Associated with a
Generalized Fibonacci Sequence . . . . . 117--126
Selmo Tauber On $Q$-Fibonacci Polynomials . . . . . . 127--134
Eugene Levine On the Generalized Langford Problem . . 135--137
Allan Scott Fibonacci Illustration of L'Hôpital's
Rule . . . . . . . . . . . . . . . . . . 138
A. P. Shah Fibonacci Sequence Modulo $m$ . . . . . 139--141
Raymond E. Whitney Advanced Problems and Solutions . . . . 142--150
Henry Winthrop Mathematical Models for the Study of the
Propagation of Novel Social Behavior . . 151--155
J. Wlodarski Curious Property of One Fraction . . . . 156
Stephen R. Cavior A Theorem on Power Sums . . . . . . . . 157--160
J. Wlodarski A Number Problem . . . . . . . . . . . . 161
Joseph S. Madachy Recreational Mathematics . . . . . . . . 162--166
M. N. S. Swamy Further Properties of Morgan--Voyce
Polynomials . . . . . . . . . . . . . . 167--175
Allan Scott Scott's Fibonacci Scrapbook . . . . . . 176
Thomas M. Green Linear Diophantine Equations with
Non-Negative Parameters and Solutions 177--184
A. P. Hillman Elementary Problems and Solutions . . . 185--191
J. Wlodarski Pascal's Triangle and Some Famous Number
Sequences . . . . . . . . . . . . . . . 192
Leon Bernstein The Linear Diophantine Equation in $n$
Variables and Its Application to
Generalized Fibonacci Numbers . . . . . 1--63
Daniel C. Fielder Special Integer Sequences Controlled by
Three Parameters . . . . . . . . . . . . 64--69
Anonymous Errata . . . . . . . . . . . . . . . . . 70
L. Carlitz Bernoulli Numbers . . . . . . . . . . . 71--84
Verner E. Hoggatt, Jr. Belated Acknowledgement . . . . . . . . 85
D. A. Lind The Quadratic Field $ Q(\sqrt {5}) $ and
a Certain Diophantine Equation . . . . . 86--93
T. W. Forget and
T. A. Larkin Pythagorean Triads of the Form $ X, X +
1, Z $ Described by Recurrence Sequences 94--104
V. E. Hoggatt, Jr. Generalized Rabbits for Generalized
Fibonacci Numbers . . . . . . . . . . . 105--192
L. Carlitz Fibonacci Representations . . . . . . . 193--220
V. E. Hoggatt, Jr. A New Angle on Pascal's Triangle . . . . 221--234
David A. Klarner Partitions of $N$ into Distinct
Fibonacci Numbers . . . . . . . . . . . 235--243
J. Wlodarski More about the ``Golden Ratio'' in the
World of Atoms . . . . . . . . . . . . . 244
Alan M. Scott Continuous Extensions of Fibonacci
Identities . . . . . . . . . . . . . . . 245--249
Raymond E. Whitney Advanced Problems and Solutions . . . . 250--260
George Ledin, Jr. Is Eratosthenes out? . . . . . . . . . . 261--265
James C. Curl Fibonacci Numbers and the Slow Learner 266--274
Joseph Mandelson Amateur Interests in the Fibonacci
Series III. Residues of $ u_n $ with
Respect to Any Modules . . . . . . . . . 275--278
Brother Alfred Brousseau Recurring Sequences --- Lesson 1 . . . . 279--285
Robert W. Prielipp Even Perfect Numbers and Seven . . . . . 286--287
A. P. Hillman Elementary Problems and Solutions . . . 288--298
Joseph S. Madachy Recreational Mathematics . . . . . . . . 299
Daniel C. Fielder Generation of Stirling Numbers by Means
of Special Partitions of Numbers . . . . 1--9
Gene B. Gale Errata for ``Factorization of $ 2 \times
2 $ Integral Matrices with Determinant $
\pm 1 $'' . . . . . . . . . . . . . . . 10
Donna B. May On a Characterization of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 11--14
Charles J. A. Halberg, Jr. The Generalized Fibonacci Operator . . . 15--33
Marjorie Bicknell A Curious Property of a Second Fraction 34
J. W. Gootherts Linear Algebra Constructed from
Fibonacci Sequences Part I: Fundamentals
and Polynomial Interpretations . . . . . 35--42
Marjorie Bicknell Romance in Mathematics . . . . . . . . . 43
J. W. Gootherts Linear Algebra Constructed from
Fibonacci Sequences. Part II: Function
Sequences and Taylor Series of Function
Sequences . . . . . . . . . . . . . . . 44--54
V. E. Hoggatt, Jr. and
D. A. Lind Symbolic Substitutions into Fibonacci
Polynomials . . . . . . . . . . . . . . 55--74
Eugene Levine Fibonacci Sequences with Identical
Characteristic Values . . . . . . . . . 75--80
C. A. Holben and
J. H. Jordan The Twin Prime Problem and Goldbach's
Conjecture in the Gaussian Integers . . 81--85
Murray S. Klamkin On the Linear Difference Equation whose
Solutions are the Products of Solutions
of Two Given Linear Difference Equations 86--92
Selmo Tauber Lah Numbers for Fibonacci and Lucas
Polynomials . . . . . . . . . . . . . . 93--99
Selmo Tauber Lah Numbers for $R$-Polynomials . . . . 100--107
Eugene Levine The Existence of Perfect $3$-Sequences 108--304
H. H. Ferns Pseudo-Fibonacci Numbers . . . . . . . . 305--317
H. W. Gould Note on a Paper of Paul F. Byrd, and a
Solution of Problem P-3 . . . . . . . . 318--321
Dov and
Moshe Jarden On the Existence of an Infinitude of
Composite Primitive Divisors of
Second-Order Recurring Sequences . . . . 322--334
D. E. Daykin and
A. J. W. Hilton Bases for Intervals of Real Numbers . . 335--349
Raymond E. Whitney Advanced Problems and Solutions . . . . 350--359
Irving Adler Three Diophantine Equations --- Part I 360--369
Donald A. Preziosi Harmonic Design in Minoan Architecture 370--384
Joseph S. Madachy Recreational Mathematics . . . . . . . . 385--389
Verner E. Hoggatt, Jr. and
Free Jamison Dissection of a Square into $n$ Acute
Isosceles Triangles . . . . . . . . . . 390--392
Brother Alfred Brousseau Linear Recursion Relations, Lesson Two 393--399
A. P. Hillman Elementary Problems and Solutions . . . 400--406
Dov Jarden Any Lucas Number $ L_{5p} $, for any
Prime $ p > 5 $, Has at Least Two
Distinct Primitive Prime Divisors . . . 407
Anonymous Volume Index . . . . . . . . . . . . . . 408
H. H. Ferns Products of Fibonacci and Lucas Numbers 1--12
Anonymous Errata . . . . . . . . . . . . . . . . . 13
A. F. Horadam Tschebyscheff and Other Functions
Associated with the Sequence $ \{ w_n(a,
b; p, q) \} $ . . . . . . . . . . . . . 14--22
H. W. Gould The Bracket Function and Fontené--Ward
Generalized Binomial Coefficients with
Application to Fibonomial Coefficients 23--40
Joseph Arkin Convergence of the Coefficients in a
Recurring Power Series . . . . . . . . . 41--55
Raymond E. Whitney Advanced Problems and Solutions . . . . 56--65
Muthulakshmi R. Iyer Identities Involving Generalized
Fibonacci Numbers . . . . . . . . . . . 66--72
Marjorie Bicknell and
Verner E. Hoggatt, Jr. Golden Triangles, Rectangles, and
Cuboids . . . . . . . . . . . . . . . . 73--91
Muthulakshmi R. Iyer Sums Involving Fibonacci Numbers . . . . 92--98
Brother Alfred Brousseau Linear Recursion Relations Lesson Three
--- The Binet Formulas . . . . . . . . . 99--104
Brother Alfred Brousseau Book Reviews: \booktitleFibonacci and
Lucas numbers, by Verner E. Hoggatt,
Jr., and \booktitleInvitation to number
theory, by Òystein Òre . . . . . . . . . . 105--106
A. P. Hillman Elementary Problems and Solutions . . . 107--112
George E. Andrews Some Formulae for the Fibonacci Sequence
with Generalizations . . . . . . . . . . 113--130
Monte B. Boisen, Jr. Overlays of Pascal's Triangle . . . . . 131--139
R. L. Duncan On the Density of the $k$-Free Integers 140--142
Brother Alfred Brousseau Summation of Infinite Fibonacci Series 143--168
Raymond E. Whitney Advanced Problems and Solutions . . . . 169--179
Edgar Karst A Four-Step Iteration Algorithm to
Generate $ x^2 $ in $ x^2 + (x + 1)^2 =
y^2 $ . . . . . . . . . . . . . . . . . 180
Irving Adler Three Diophantine Equations --- Part II 181--193
Brother Alfred Brousseau Linear Recursion Relations --- Lesson
Four Second-Order Linear Recursion
Relations . . . . . . . . . . . . . . . 194--200
Muthulakshmi R. Iyer Some Results on Fibonacci Quaternions 201--210
Brother Alfred Brousseau Fibonacci--Lucas Infinite Series
Research Topic . . . . . . . . . . . . . 211--217
A. P. Hillman Elementary Problems and Solutions . . . 218--224
Muthulakshmi R. Iyer A Note on Fibonacci Quaternions . . . . 225--229
Emanuel Vegh Remark on a Theorem by Waksman . . . . . 230
Edgar I. Emerson Recurrent Sequences in the Equation $ D
Q^2 = R^2 + N $ . . . . . . . . . . . . 231--242
J. L. Brown, Jr. Unique Representations of Integers as
Sums of Distinct Lucas Numbers . . . . . 243--251
Anonymous Association Meeting . . . . . . . . . . 252
V. E. Hoggatt, Jr. and
D. A. Lind Compositions and Fibonacci Numbers . . . 253--266
P. Erd\Hos and
I. Kátai On the Growth of $ d_k(n) $ . . . . . . 267--274
N. A. Draim $ \pi $ in the Form of a Continued
Fraction with Infinite Terms . . . . . . 275--276
Raymond E. Whitney Advanced Problems and Solutions . . . . 277--283
Anonymous Corrections . . . . . . . . . . . . . . 284--286
Charles W. Trigg Associated Additive Decimal Digital
Bracelets . . . . . . . . . . . . . . . 287--294
Brother Alfred Brousseau Linear Recursion Relations --- Lesson
Five Recursion Relations of Higher Order 295--300
Marjorie Bicknell A Note on Fibonacci Numbers in High
School Algebra . . . . . . . . . . . . . 301--302
John Ivie Multiple Fibonacci Sums . . . . . . . . 303--309
Olov Alvfeldt A Brain Teaser Related to Fibonacci
Numbers . . . . . . . . . . . . . . . . 310--314
Joseph S. Madachy Recreational Mathematics ---
``Difference Series'' Resulting from
Sieving Primes . . . . . . . . . . . . . 315--318
D. V. Jaiswal On Determinants Involving Generalized
Fibonacci Numbers . . . . . . . . . . . 319--330
A. P. Hillman Elementary Problems and Solutions . . . 331--336
Dale D. Shea On the Number of Divisions Needed in
Finding the Greatest Common Divisor . . 337--340
V. E. Hoggatt, Jr. and
Marjorie Bicknell Diagonal Sums of Generalized Pascal
Triangles . . . . . . . . . . . . . . . 341--358
L. Carlitz Generating Functions . . . . . . . . . . 359--393
Leon Bernstein and
Helmut Hasse Explicit Determination of the Perron
Matrices in Periodic Algorithms of the
Perron--Jacobi Type with Application to
Generalized Fibonacci Numbers with Time
Impulses . . . . . . . . . . . . . . . . 394--436
V. R. Rao Uppuluri and
John A. Carpenter Numbers Generated by the Function $ \exp
(1 - e^x) $ . . . . . . . . . . . . . . 437--448
Edward A. Parberry A Recursion Relation for Populations of
Diatoms . . . . . . . . . . . . . . . . 449--456
W. A. Webb and
E. A. Parberry Divisibility Properties of Fibonacci
Polynomials . . . . . . . . . . . . . . 457--463
D. E. Daykin On the Completeness of the Lucas
Sequence . . . . . . . . . . . . . . . . 464
L. Kuipers Remark on a Paper by R. L. Duncan
Concerning the Uniform Distribution Mod
$1$ of the Sequence of the Logarithms of
the Fibonacci Numbers . . . . . . . . . 465--466
L. Carlitz and
J. A. H. Hunter Sums of Powers of Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 467--473
R. L. Duncan Note on the Initial Digit Problem . . . 474--475
Hymie London and
Raphael Finkelstein On Fibonacci and Lucas Numbers Which are
Perfect Powers . . . . . . . . . . . . . 476--481
V. E. Hoggatt, Jr. and
D. A. Lind The Dying Rabbit Problem . . . . . . . . 482--487
J. C. Ahuja Orthogonal Expansion Derived from the
Extreme Value Distribution . . . . . . . 488--493
D. E. Daykin Representation of Natural Numbers as
Sums of Generalized Fibonacci Numbers
--- II . . . . . . . . . . . . . . . . . 494--510
Raymond E. Whitney Advanced Problems and Solutions . . . . 511--522
H. E. Huntley Fibonacci and the Atom . . . . . . . . . 523--524
Brother Alfred Brousseau Fibonacci Statistics in Conifers . . . . 525--532
Brother Alfred Brousseau Linear Recursion Relations --- Lesson
Six Combining Linear Recursion Relations 533--537
Irving Adler A Shorter Proof . . . . . . . . . . . . 538
Bruce W. King and
Francis D. Parker A Fibonacci Matrix and the Permanent
Function . . . . . . . . . . . . . . . . 539--544
A. P. Hillman Elementary Problems and Solutions . . . 545--551
Anonymous Volume Index . . . . . . . . . . . . . . 552
Sidney Kravitz The Lucas--Lehmer Test for Mersenne
Numbers . . . . . . . . . . . . . . . . 1--3
Joseph Arkin and
Richard Pollack Recurrence Formulas . . . . . . . . . . 4--5
W. C. Lynch The $t$-Fibonacci Numbers and Polyphase
Sorting . . . . . . . . . . . . . . . . 6--22
D. E. Daykin and
L. A. G. Dresel Factorization of Fibonacci Numbers . . . 23--30
Hyman Gabai Generalized Fibonacci $k$-Sequences . . 31--38
R. J. Weinshenk and
V. E. Hoggatt, Jr. On Solving $ C_{n + 2} = C_{n + 1} + C_n
+ n^m $ by Expansions and Operators . . 39--48
Edward A. Parberry On Primes and Pseudo-Primes Related to
the Fibonacci Sequence . . . . . . . . . 49--60
L. Carlitz and
H. H. Ferns Some Fibonacci and Lucas Identities . . 61--73
Raymond E. Whitney Advanced Problems and Solutions . . . . 74--82
Rodney T. Hansen Arithmetic of Pentagonal Numbers . . . . 83--86
Anonymous Corrections . . . . . . . . . . . . . . 87
Anonymous Letters to the Editor . . . . . . . . . 88--89
Jean H. Anderson Spirals, Checkerboards, Polyominoes, and
the Fibonacci Sequence . . . . . . . . . 90--95
Brother Alfred Brousseau Linear Recursion Relations --- Lesson
Seven Analyzing Linear Recursion
Relations . . . . . . . . . . . . . . . 96--101
V. C. Harris An Algorithm for Finding the Greatest
Common Divisor . . . . . . . . . . . . . 102--103
V. C. Harris Note on the Number of Divisions Required
in Finding the Greatest Common Divisor 104
A. P. Hillman Elementary Problems and Solutions . . . 105--112
L. Carlitz Fibonacci Representations --- II . . . . 113--134
C. T. Long and
J. H. Jordan A Limited Arithmetic on Simple Continued
Fractions --- II . . . . . . . . . . . . 135--157
Verner E. Hoggatt, Jr. Convolution Triangles for Generalized
Fibonacci Numbers . . . . . . . . . . . 158--171
Rosedith Sitgreaves Some Properties of Stirling Numbers of
the Second Kind . . . . . . . . . . . . 172--181
D. J. DeCarli A Generalized Fibonacci Sequence over an
Arbitrary Ring . . . . . . . . . . . . . 182--184
S. K. Zaremba A Remarkable Lattice Generated by
Fibonacci Numbers . . . . . . . . . . . 185--198
Joseph Arkin and
Verner E. Hoggatt, Jr. An Extension of Fibonacci Numbers --- II 199--216
Gottfried Bruckner Fibonacci Sequence Modulo a Prime $ p
\equiv 3 \pmod {4} $ . . . . . . . . . . 217--220
N. A. Draim and
Marjorie Bicknell Summation of Powers of Roots of Special
Equations . . . . . . . . . . . . . . . 221--224
Allen J. Schwenk Take-Away Games . . . . . . . . . . . . 225--234
C. A. Church, Jr. On the Enumeration of Certain Triangular
Arrays . . . . . . . . . . . . . . . . . 235--241
Nannette Cox and
John W. Phillips and
V. E. Hoggatt, Jr. Some Universal Counterexamples . . . . . 242--247
Anonymous Corrections . . . . . . . . . . . . . . 248
L. Carlitz Some Generalized Fibonacci Identities 249--254
H. P. Yap A Simple Recurrence Relation on Finite
Abelian Groups . . . . . . . . . . . . . 255--263
David Singmaster Some Counterexamples and Problems on
Linear Recurrence Relations . . . . . . 264--267
Raymond E. Whitney Advanced Problems and Solutions . . . . 268--279
Brother Alfred Brousseau Book Review: \booktitleLeonard of Pisa
and the new mathematics of the Middle
Ages, by Joseph Gies and Frances Gies 280
Richard E. M. Moore Mosaic Units: Pattern Sizes in Ancient
Mosaics . . . . . . . . . . . . . . . . 281--310
Brother Alfred Brousseau Linear Recursion Relations --- Lesson
Eight Asymptotic Ratios in Recursion
Relations . . . . . . . . . . . . . . . 311--316
Edgar Karst Magic Squares Consisting of Primes in A.
P. . . . . . . . . . . . . . . . . . . . 317--324
A. P. Hillman Elementary Problems and Solutions . . . 325--334
Dorothy Fifield Ups and Downs . . . . . . . . . . . . . 335
Anonymous Association Meeting . . . . . . . . . . 336
D. Suryanarayana and
Peter Hagis, Jr. A Theorem Concerning Odd Perfect Numbers 337--346
D. E. Daykin An Addition Algorithm for Greatest
Common Divisor . . . . . . . . . . . . . 347--349
David Zeitlin On Determinant Whose Elements are
Products of Recursive Sequences . . . . 350--359
Verner E. Hoggatt, Jr. An Application of the Lucas Triangle . . 360--364
Eugene A. Maier One-One Correspondences Between the Set
$N$ of Positive Integers and the Sets $
N^n $ and $ \cup_{n \in N} N^n $ . . . . 365--370
Brother L. Raphael Some Results in Trigonometry . . . . . . 371
R. G. Buschman The ``Difference Series'' of Madachy . . 372--374
Kenneth B. Stolarsky Infinitely Many Generalizations of
Abel's Partial Summation Identity . . . 375--379
K. U. Lu The Smallest Number with Divisors a
Product of Distinct Primes . . . . . . . 380--382
Raymond E. Whitney Advanced Problems and Solutions . . . . 383--392
Janet Waterman Glaze Angle Multisection by Parallel
Straightedges (Recreational Mathematics
Edited by Joseph S. Madachy) . . . . . . 393--396
W. R. Spickerman A Note on Fibonacci Functions . . . . . 397--401
Ernst M. Cohn Complete Diophantine Solution of the
Pythagorean Triple . . . . . . . . . . . 402--405
J. A. H. Hunter Fibonacci to the Rescue . . . . . . . . 406
Marjorie Bicknell A Primer for the Fibonacci Numbers ---
Part VII . . . . . . . . . . . . . . . . 407--420
Joseph Arkin An Extension of a Theorem of Euler . . . 421--427
B. A. Read Fibonacci Series in the Solar System . . 428--438
Brother Alfred Brousseau A Lucas Analogue . . . . . . . . . . . . 439--442
A. P. Hillman Elementary Problems and Solutions . . . 443--448
D. A. Lind A Fibonacci Circulant . . . . . . . . . 449--455
Verner E. Hoggatt, Jr. Combinatorial Problems for Generalized
Fibonacci Numbers . . . . . . . . . . . 456--462
Raphael Finkelstein and
Edgar Karst and
Hymie London Application of Recursive Sequences to
Diophantine Equations . . . . . . . . . 463--469
Raymond E. Whitney On a Class of Difference Equations . . . 470--474
David G. Beverage On a Conjecture of Dmitri Thoro . . . . 475
Morris Jack DeLeon The Fibonacci Numbers Considered as a
Pisot Sequence . . . . . . . . . . . . . 476--480
Anonymous Fall's Research Conference . . . . . . . 481
J. L. Brown, Jr. and
R. L. Duncan Modulo One Uniform Distribution of the
Sequence of Logarithms of Certain
Recursive Sequences . . . . . . . . . . 482--486
Raymond E. Whitney Advanced Problems and Solutions . . . . 487--497
David G. Beverage Letter to the Editor . . . . . . . . . . 498
John H. Carlson Determination of Heronian Triangles . . 499--506
Philip B. Onderdonk Pineapples and Fibonacci Numbers . . . . 507--508
J. M. Williams, Jr. The Powers of Three . . . . . . . . . . 509--515
Joe R. Crenshaw Some Remarks on the Ordering of General
Fibonacci Sequences . . . . . . . . . . 516--521
John B. Lewis The Educational Value in Mathematics . . 522--529
Anonymous Errata . . . . . . . . . . . . . . . . . 530
Joseph Arkin Certain Arithmetical Properties of $ 0.5
k (a k + 1) $ . . . . . . . . . . . . . 531--537
Edward T. Frankel Fibonacci Numbers as Paths of Rooks on a
Chessboard . . . . . . . . . . . . . . . 538--541
A. P. Hillman Elementary Problems and Solutions . . . 542--551
Anonymous Volume Index . . . . . . . . . . . . . . 552
V. E. Hoggatt, Jr. and
John W. Phillips and
H. T. Leonard, Jr. Twenty-Four Master Identities . . . . . 1--17
W. A. Al-Salam and
A. Verma Fibonacci Numbers and Eulerian
Polynomials . . . . . . . . . . . . . . 18--22
Sister Christelle Theusch Composition of $ \Phi_2 (x) $ Modulo $m$ 23--27
L. Carlitz Some Summation Formulas . . . . . . . . 28--33
David Zeitlin Letter to the Editor . . . . . . . . . . 34
James E. Desmond On Iterative Fibonacci Subscripts . . . 35--40
Robert M. Giuli Binet Forms by Laplace Transform . . . . 41--50
A. P. Hillman and
P. L. Mana and
C. T. McAbee A Symmetric Substitute for Stirling
Numbers . . . . . . . . . . . . . . . . 51--60
Raymond E. Whitney Advanced Problems and Solutions . . . . 61--73
Marjorie Bicknell A Primer for Fibonacci Numbers: Part
VIII . . . . . . . . . . . . . . . . . . 74--80
Anonymous Errata . . . . . . . . . . . . . . . . . 81
J. Wlodarski The Possible End of the Periodic Table
of Elements and the ``Golden Ratio'' . . 82
Harlan Umansky Pythagoras Revisited . . . . . . . . . . 83--86
J. Wlodarski Fibonacci and Lucas Numbers Tend to Obey
Benford's Law . . . . . . . . . . . . . 87--88
Underwood Dudley and
Bessie Tucker Greatest Common Divisors in Altered
Fibonacci Sequences . . . . . . . . . . 89--92
Phil Lafer Discovering the Square-Triangular
Numbers . . . . . . . . . . . . . . . . 93--105
A. P. Hillman Elementary Problems and Solutions . . . 106--112
D. A. Lind A Determinant Involving Generalized
Binomial Coefficients . . . . . . . . . 113--119
V. E. Hoggatt, Jr. and
Walter Hansell The Hidden Hexagon Squares . . . . . . . 120
Verner E. Hoggatt, Jr. Some Special Fibonacci and Lucas
Generating Functions . . . . . . . . . . 121--133
Raymond E. Whitney Advanced Problems and Solutions . . . . 134--145
J. Wlodarski Regular Polyhedrons and Pascal's
Triangle . . . . . . . . . . . . . . . . 146
Irving Adler Sequences with a Characteristic Number 147--162
Joseph P. Munzenrider A New Anthesis . . . . . . . . . . . . . 163--176
Sal LaBarbera Fibonacci, Lucas and the Egyptians . . . 177--187
J. Wlodarski The Golden Ratio in an Electrical
Network . . . . . . . . . . . . . . . . 188
Charles W. Trigg Kaprekar's Routine with Two-Digit
Integers . . . . . . . . . . . . . . . . 189--194
J. Wlodarski A Number Problem . . . . . . . . . . . . 195
R. L. Bauer Numbers that are Both Triangular and
Square Their Triangular Roots and Square
Roots . . . . . . . . . . . . . . . . . 196--198
Jean J. Pedersen Asymptotic Euclidean Type Constructions
without Euclidean Tools (Recreational
Mathematics Edited by Joseph S. Madachy) 199--216
A. P. Hillman Elementary Problems and Solutions . . . 217--224
Morton Abramson Combinations, Compositions and Occupancy
Problems . . . . . . . . . . . . . . . . 225--236
T. Antony Davis Why Fibonacci Sequence for Palm Leaf
Spirals? . . . . . . . . . . . . . . . . 237--244
A. F. Horadam Pell Identities . . . . . . . . . . . . 245--252
T. Antony Davis and
T. K. Bose Fibonacci System in Aroids . . . . . . . 253--263
J. E. Walton and
A. F. Horadam Some Properties of Certain Generalized
Fibonacci Matrices . . . . . . . . . . . 264--276
André Gougenheim About the Linear Sequence of the
Integers Such That Each Term is the Sum
of the Two Preceding . . . . . . . . . . 277--295
Max Rumney and
E. J. F. Primrose Relations Between a Sequence of
Fibonacci Type and the Sequence of its
Partial Sums . . . . . . . . . . . . . . 296--298
A. G. Shannon and
A. F. Horadam Reciprocals of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 299--306
A. G. Shannon and
A. F. Horadam A Generalized Pythagorean Theorem . . . 307--312
W. Jentsch On an Initial-Value Problem for Linear
Partial Difference Equations . . . . . . 313--323
D. Mangeron and
M. N. Oguztorelli and
V. E. Poterasu On the Generation of Fibonacci Numbers
and the ``Polyvibrating'' Extension of
These Numbers . . . . . . . . . . . . . 324--328
C. C. Cadogan On Partly Ordered Partitions of a
Positive Integer . . . . . . . . . . . . 329--336
H. W. Gould Equal Products of Generalized Binomial
Coefficients . . . . . . . . . . . . . . 337--346
J. L. Brown, Jr. and
R. L. Duncan The Least Remainder Algorithm . . . . . 347--350
V. E. Hoggatt, Jr. and
G. L. Alexanderson A Property of Multinomial Coefficients 351--356
David Zeitlin General Identities for Recurrent
Sequences of Order Two . . . . . . . . . 357--388
Raymond E. Whitney Advanced Problems and Solutions . . . . 389--401
Wray G. Brady Additions to the Summation of Reciprocal
Fibonacci and Lucas Series . . . . . . . 402--404
Robert C. Good, Jr. A Series Form for the Fibonacci Numbers
$ F_{12n} $ . . . . . . . . . . . . . . 405--411
Anonymous Program of the Eigth Anniversary Meeting 412
W. C. Barley Triangles de Fibonacci . . . . . . . . . 413--422
Edward L. Lowman An Example of Fibonacci Numbers Used to
Generate Rhythmic Values in Modern Music 423--426
Brother Alfred Brousseau Continued Fractions of Quadratic
Fibonacci Ratios . . . . . . . . . . . . 427--436
V. E. Hoggatt, Jr. Some More Fibonacci Diophantine
Equations . . . . . . . . . . . . . . . 437
A. P. Hillman Elementary Problems and Solutions . . . 438--448
L. Carlitz Reduction Formulas for Fibonacci
Summations . . . . . . . . . . . . . . . 449--466
M. Beresin and
E. Levine and
D. Lubell On the Coefficients of a Generating
Series . . . . . . . . . . . . . . . . . 467--476
J. L. Brown, Jr. On Generalized Bases for Real Numbers 477--496
S. A. Burr On Moduli for which the Fibonacci
Sequence Contains a Complete System of
Residues . . . . . . . . . . . . . . . . 497--503
Anonymous Ninth Annual Fall Conference of the
Fibonacci Association . . . . . . . . . 504
C. A. Church, Jr. Combinations and Their Duals . . . . . . 505--511
Raymond E. Whitney Advanced Problems and Solutions . . . . 512--524
John Brillhart and
Emma Lehmer Challenge . . . . . . . . . . . . . . . 525
Frederick Stern The Sum of the First $n$ Positive
Numbers --- Geometrically . . . . . . . 526
Edward A. Lowman Some Striking Proportions in the Music
of Bela Bartók . . . . . . . . . . . . . 527--528
Marjorie Bicknell and
Verner E. Hoggatt, Jr. A Primer for the Fibonacci Numbers: Part
IX . . . . . . . . . . . . . . . . . . . 529--537
Marjorie Bicknell A Fibonacci Crostic . . . . . . . . . . 538--540
David Beverage A Polynomial Representation of Fibonacci
Numbers . . . . . . . . . . . . . . . . 541--544
A. P. Hillman Elementary Problems and Solutions . . . 545--551
Anonymous Volume Index . . . . . . . . . . . . . . 552
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Fibonacci Representations . . . . . . . 1--28
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Lucas Representations . . . . . . . . . 29--42
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Fibonacci Representations of Higher
Order . . . . . . . . . . . . . . . . . 43--70
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Fibonacci Representations of Higher
Order --- II . . . . . . . . . . . . . . 71--80
V. E. Hoggatt, Jr. and
Brian Peterson Some General Results on Representations 81--88
V. E. Hoggatt, Jr. Generalized Zeckendorf Theorem . . . . . 89--94
Timothy J. Keller Generalizations of Zeckendorf's Theorem 95--102
Roger O'Connell Representations of Integers as Sums of
Fibonacci Squares . . . . . . . . . . . 103--112
Christoph Witzgall Fibonacci Search with Arbitrary First
Evaluation . . . . . . . . . . . . . . . 113--134
A. G. Shannon and
A. F. Horadam Some Properties of Third-Order
Recurrence Relations . . . . . . . . . . 135--146
Marjorie Bicknell Determinants and Identities Involving
Fibonacci Squares . . . . . . . . . . . 147--156
L. Carlitz A Generating Function for Partly Ordered
Partitions . . . . . . . . . . . . . . . 157--162
Daniel Shanks Fibonacci Primitive Roots . . . . . . . 163--168
Paul S. Bruckman An Interesting Sequence of Numbers
Derived From Various Generating
Functions . . . . . . . . . . . . . . . 169--181
Brother Alfred Brousseau Table of Indices with a Fibonacci
Relation . . . . . . . . . . . . . . . . 182--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--196
Brother Alfred Brousseau Fibonacci Magic Cards . . . . . . . . . 197
Anonymous Corrections . . . . . . . . . . . . . . 198
Wray G. Brady The Lambert Function . . . . . . . . . . 199--200
J. A. H. Hunter Fibonacci Once Again . . . . . . . . . . 201--202
Harlan L. Umansky A Note on Pythagorean Triplets . . . . . 203--206
Robert Anaya and
Janice Crump A Generalized Greatest Integer Function
Theorem . . . . . . . . . . . . . . . . 207--212
J. A. H. Hunter and
Joseph S. Madachy Back-to-Back: Some Interesting
Relationships Between Representations of
Integers In Various Bases . . . . . . . 213--217
A. P. Hillman Elementary Problems and Solutions . . . 218--224
John C. Higgins Subsemigroups of the Additive Positive
Integers . . . . . . . . . . . . . . . . 225--230
C. C. Yalavigi Properties of Tribonacci Numbers . . . . 231--246
Brother Alfred Brousseau Note on the Characteristic Number of a
Sequence of Fibonacci Squares . . . . . 247--248
P. Erd\Hos and
R. L. Graham On Sums of Fibonacci Numbers . . . . . . 249--254
John Ivie A General $Q$-Matrix . . . . . . . . . . 255--261
Leslie E. Blumenson A Characterization of Fibonacci Numbers
Suggested by a Problem in Cancer
Research . . . . . . . . . . . . . . . . 262--264
Robert M. Giuli Linear Homogeneous Difference Equations 265--270
V. E. Hoggatt, Jr. Generalized Fibonacci Numbers in
Pascal's Pyramid . . . . . . . . . . . . 271--276
J. L. Brown, Jr. and
R. L. Duncan Modulo One Uniform Distribution of
Certain Fibonacci-Related Sequences . . 277--280
L. Carlitz Note on Summation Formulas . . . . . . . 281--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--294
Joseph S. Madachy Some New Narcissistic Numbers . . . . . 295--298
Rolf A. Deininger Fibonacci Numbers and Water Pollution
Control . . . . . . . . . . . . . . . . 299--300
J. Wlodarski A Number Game . . . . . . . . . . . . . 301--302
Brother Alfred Brousseau Fibonacci Numbers and Geometry . . . . . 303--318
Hugo Norden Proportions and the Composer . . . . . . 319--323
M. S. Klamkin A Number Problem . . . . . . . . . . . . 324
Beverly Ross A Lucas Number Counting Problem . . . . 325--327
Anonymous Corrigenda . . . . . . . . . . . . . . . 328
A. P. Hillman Elementary Problems and Solutions . . . 329--336
P. S. Fisher and
E. E. Kohlbecker A Generalized Fibonacci Sequence . . . . 337--344
Lawrence F. Somer The Fibonacci Group and a New Proof that
$ F_{p - (5 / p)} \equiv 0 \pmod {p} $ 345--348
J. M. Gandhi and
V. S. Taneja The Coefficients of $ \cosh x / \cos x $ 349--354
H. W. Gould A New Primality Criterion of Mann and
Shanks and its Relation to a Theorem of
Hermite with Extension to Fibonomials 355--364
E. Zeckendorf A Generalized Fibonacci Numeration . . . 365--372
Harald Niederreiter Distribution of Fibonacci Numbers Mod $
5^k $ . . . . . . . . . . . . . . . . . 373--374
Lawrence Kuipers and
Jau-shyong Shiue A Distribution Property of the Sequence
of Fibonacci Numbers . . . . . . . . . . 375--376
Gerald Edgar Perfect $N$-Sequences for $N$, $ N + 1
$, and $ N + 2 $ . . . . . . . . . . . . 377--380
H. W. Gould The Case of the Strange Binomial
Identities of Professor Moriarty . . . . 381--392
Nicholas P. Callas Representations of Automorphic Numbers 393--396
David Zeitlin A Product Identity for Sequences Defined
by $ W_{n + 2} = d W_{n + 1} - c W_n $ 397--402
Ernst M. Cohn Pell Number Triples . . . . . . . . . . 403--404
H. C. Williams Fibonacci Numbers Obtained from Pascal's
Triangle with Generalizations . . . . . 405--412
Raymond E. Whitney Advanced Problems and Solutions . . . . 413--421
Rex H. Shudde Golden Section Search Problem . . . . . 422
Brother L. Raphael and
FSC Introduction to Patton Polygons . . . . 423--428
Brother Alfred Brousseau Algorithm for Analyzing a Linear
Recursion Sequence . . . . . . . . . . . 429--432
V. E. Hoggatt, Jr. and
Marjorie Bicknell Fun with Fibonacci at the Chess Match 433--434
Andrew Feinberg Polyhedra, Pentagrams and Plato . . . . 435--438
Joseph L. Ercolano Making Golden Cuts with a Shoemaker's
Knife . . . . . . . . . . . . . . . . . 439--440
Brother Alfred Brousseau Ye Olde Fibonacci Curiosity Shoppe . . . 441--443
Marjorie Bicknell Book Review: \booktitleA Mathematical
model of life and living, by Li-kung
Shaw . . . . . . . . . . . . . . . . . . 444--444
Anonymous Program of the Ninth Anniversary Meeting 445--446
A. P. Hillman Elementary Problems and Solutions . . . 447
Anonymous Errata . . . . . . . . . . . . . . . . . 448--453
Anonymous Fibonacci Makes the Sports Page . . . . 454
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Pellian Representations . . . . . . . . 449--488
L. Carlitz Enumeration of $ 3 \times 3 $ Arrays . . 489--498
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Representations for a Special Sequence 499--518
Judy Kramer and
V. E. Hoggatt, Jr. Special Cases of Fibonacci Periodicity 519--522
L. Carlitz Concavity Properties of Certain
Sequences of Numbers . . . . . . . . . . 523--525
L. Carlitz A Conjecture Concerning Lucas Numbers 526
L. Carlitz and
Richard Scoville and
V. E. Hoggatt, Jr. Addendum to the Paper ``Fibonacci
Representations'' . . . . . . . . . . . 527--530
L. Carlitz Sequences, Paths, Ballot Numbers . . . . 531--550
V. E. Hoggatt, Jr. and
Bob Chow Some Theorems on Completeness . . . . . 551--554
V. E. Hoggatt, Jr. and
Marjorie Bichnell and
Ellen L. King Fibonacci and Lucas Triangles . . . . . 555--560
I. McCausland A Simple Optimal Control Sequence in
Terms of Fibonacci Numbers . . . . . . . 561--564
A. P. Hillman and
V. E. Hoggatt, Jr. A Proof of Gould's Pascal Hexagon
Conjecture . . . . . . . . . . . . . . . 565--568
Janos Galambos A Constructive Uniqueness Theorem on
Representing Integers . . . . . . . . . 569--570
Rodney T. Hansen Generating Identities for Fibonacci and
Lucas Triples . . . . . . . . . . . . . 571--578
H. W. Gould A New Greatest Common Divisor Property
of the Binomial Coefficients . . . . . . 579--584
L. R. Shenton Linear Difference Equations and
Generalized Continuants Part I:
Algebraic Developments . . . . . . . . . 585--590
L. Carlitz and
D. P. Roselle Triangular Arrays Subject to MacMahon's
Conditions . . . . . . . . . . . . . . . 591--598
Verner E. Hoggatt, Jr. and
Marjorie Bicknell Convolution Triangles . . . . . . . . . 599--608
Hwa S. Hahn A Counting Function of Integral
$n$-Triples . . . . . . . . . . . . . . 609--612
H. W. Gould Some Combinatorial Identities of
Bruckman --- a Systematic Treatment with
Relation to the Older Literature . . . . 613--628
Raymond E. Whitney Advanced Problems and Solutions . . . . 629--642
W. E. Sharp Fibonacci Drainage Patterns . . . . . . 643--646
Brother Alfred Brousseau A Primer for the Fibonacci Numbers. Part
X: On the Representation of Integers . . 647--650
Edgar Karst More About Magic Squares Consisting of
Different Primes . . . . . . . . . . . . 651--655
Anonymous Errata . . . . . . . . . . . . . . . . . 656
Brother Alfred Brousseau A Note on the Number of Fibonacci
Sequences . . . . . . . . . . . . . . . 657--658
Basil Davis Fibonacci Numbers in Physics . . . . . . 659--660
Reuven Peleg An Old Fibonacci Formula and Stopping
Rules . . . . . . . . . . . . . . . . . 661
Anonymous Announcement . . . . . . . . . . . . . . 662
A. P. Hillman Elementary Problems and Solutions . . . 663--666
Anonymous Volume Index . . . . . . . . . . . . . . 667
Helaman Rolfe Pratt Ferguson Bernoulli Numbers and Non-Standard
Differentiable Structures on $ (4 k - 1)
$-Spheres . . . . . . . . . . . . . . . 1--14
Joseph Arkin Convergence of the Coefficients in the
$k$ th Power of a Power Series . . . . . 15--24
E. G. Straus On the Greatest common Divisor of Some
Binomial Coefficients . . . . . . . . . 25--26
H. W. Gould A Triangle with Integral Sides and Area 27--39
N. T. Gridgeman A New Look at Fibonacci Generalization 40--54
Anonymous Fibonacci Association Meeting:
Conference Program . . . . . . . . . . . 55
E. P. Merkes and
David Meyers On the Length of the Euclidean Algorithm 56--61
David Zeitlin Letter to the Editor . . . . . . . . . . 62
Ernst M. Cohn Letter to the Editor . . . . . . . . . . 62
Herta T. Freitag On Summations and Expansions of
Fibonacci Numbers . . . . . . . . . . . 63--71
Raymond E. Whitney Advanced Problems and Solutions . . . . 72--77
Dianne Smith Lucas Numbers Common to Two Polygonal
Sequences . . . . . . . . . . . . . . . 78--84
Verner E. Hoggatt, Jr. and
Janet Crump Anaya A Primer for the Fibonacci Numbers. Part
XI: Multisection Generating Functions
for the Columns of Pascal's Triangle . . 85--90
Brother Alfred Brousseau and
Harold Andersen and
Jerome Povse A Curious Property of Unit Fractions of
the Form $ 1 / d $ Where $ (d, 10) = 1 $ 91--98
Richard E. Grimm The Autobiography of Leonardo Pisano . . 99--104
A. P. Hillman Elementary Problems and Solutions . . . 105--112
L. Carlitz Enumeration of Two-Line Arrays . . . . . 113--130
Marjorie Bicknell and
V. E. Hoggatt, Jr. Unit Determinants in Generalized Pascal
Triangles . . . . . . . . . . . . . . . 131--144
S. K. Stein The Density of the Product of Arithmetic
Progression . . . . . . . . . . . . . . 145--152
Selmo Tauber $n$-Fibonacci Products . . . . . . . . . 153--156
David Singmaster Some Corrections to Carlson's
``Determination of Heronian Triangles'' 157--158
Daniel Shanks and
Larry Taylor An Observation of Fibonacci Primitive
Roots . . . . . . . . . . . . . . . . . 159--160
Hugo S. Sun A Group-Theoretical Proof of a Theorem
in Elementary Number Theory . . . . . . 161
Anonymous Errata . . . . . . . . . . . . . . . . . 162
C. C. Yalavigi Periodicity of Second- and Third-Order
Recurring Sequences . . . . . . . . . . 163--165
Murray S. Klamkin On Solving non-Homogeneous Linear
Difference Equations . . . . . . . . . . 166--168
Murray S. Klamkin and
R. S. Fishman A Reliability Problem . . . . . . . . . 169--173
Joseph Arkin The First Solution of the Classical
Eulerian Magic Cube Problem of Order Ten 174--178
Selmo Tauber On $K$-Numbers . . . . . . . . . . . . . 179--183
Raymond E. Whitney Advanced Problems and Solutions . . . . 184--188
Brother Alfred Brousseau Through the Other End of the Telescope 189--194
G. D. (Don) Chakerian The Golden Ratio and a Greek Crisis . . 195--200
Frederick Stern Intersections of Lines Connecting Two
Parallel Lines . . . . . . . . . . . . . 201--203
Joseph L. Ercolano A Geometric Treatment of Some of the
Algebraic Properties of the Golden
Section . . . . . . . . . . . . . . . . 204--208
Brother Alfred Brousseau Generalized Fibonacci Shift Formulas . . 209--223
A. P. Hillman Elementary Problems and Solutions . . . 224
Paul S. Bruckman Some Generalizations Suggested by
Gould's Systematic Treatment of Certain
Binomial Identities . . . . . . . . . . 225--240
F. W. Light, Jr. A Procedure for the Enumeration of $ 4
\times n $ Latin Rectangles . . . . . . 241--246
R. G. Buschman Some Simple Sieves . . . . . . . . . . . 247--254
Haruo Hosoya Topological Index and Fibonacci Numbers
with Relation to Chemistry . . . . . . . 255--265
Marjorie Bicknell Book Review: \booktitleI Ching Games, by
H. Y. Li and Sibley S. Morrill . . . . . 266
David A. Klarner The Number of SDR's in Certain Regular
Systems . . . . . . . . . . . . . . . . 267--270
V. E. Hoggatt, Jr. and
Marjorie Bicknell Roots of Fibonacci Polynomials . . . . . 271--274
C. A. Church and
Marjorie Bicknell Exponential Generating Functions for
Fibonacci Identities . . . . . . . . . . 275--281
David Singmaster Notes on Binomial Coefficients: IV ---
Proof of a Conjecture of Gould on the
GCD's of Two Triples of Binomial
Coefficients . . . . . . . . . . . . . . 282--283
Anonymous Letters to the Editors . . . . . . . . . 284
Bjarne Junge and
V. E. Hoggatt, Jr. Polynomials Arising from Reflections
across Multiple Plates . . . . . . . . . 285--291
L. Kuipers and
Jau-shyong Shiue Remark on a Paper by Duncan and Brown on
the Sequence of Logarithms of Certain
Recursive Sequences . . . . . . . . . . 292--293
Anonymous Errata . . . . . . . . . . . . . . . . . 294
R. G. Buschman Representations as Products or as Sums 295--301
Leo Moser and
Max Wyman Multiple Reflections . . . . . . . . . . 302--306
Dean R. Hickerson Recursion-Type Formulae for Partitions
into Distinct Parts . . . . . . . . . . 307--311
Raymond E. Whitney Advanced Problems and Solutions . . . . 312--314
D. A. Butter An Inequality in a Certain Diophantine
Equation . . . . . . . . . . . . . . . . 315--316
Verner E. Hoggatt, Jr. and
Nannette Cox and
Marjorie Bicknell A Primer for the Fibonacci Numbers: Part
XII . . . . . . . . . . . . . . . . . . 317--331
Brother Alfred Brousseau Ye Olde Fibonacci Curiosity Shoppe . . . 332
A. P. Hillman Elementary Problems and Solutions . . . 333--336
L. Carlitz and
Richard Scoville and
Theresa Vaughan Some Arithmetic Function Related to
Fibonacci Numbers . . . . . . . . . . . 337--386
J. L. Hunsucker and
W. P. Wardlaw Complete Sequences of Fibonacci Powers 387--394
Verner E. Hoggatt, Jr. and
Danial C. Fielder Analytical Verification of an ``at
Sight'' Transformation . . . . . . . . . 395--398
Verner E. Hoggatt, Jr. and
Marjorie Bicknell Generalized Fibonacci Polynomials and
Zeckendorf's Theorem . . . . . . . . . . 399--419
Daniel C. Fielder A Discussion of Subscript Sets with Some
Fibonacci Counting Help . . . . . . . . 420--428
A. V. Aho and
N. J. A. Sloane Some Doubly Exponential Sequences . . . 429--437
Sol Weintraub On Storing and Analyzing Large Strings
of Primes . . . . . . . . . . . . . . . 438--440
Daniel C. Fielder Counting of Certain Partitions of
Numbers . . . . . . . . . . . . . . . . 441--442
Graham Lord Counting Omitted Values . . . . . . . . 443--448
Calvin T. Long Arrays of Binomial Coefficients Whose
Products are Squares . . . . . . . . . . 449--456
Marjorie Bicknell and
V. E. Hoggatt, Jr. Generalized Fibonacci Polynomials . . . 457--465
R. J. DeCarli Periodicity Over the Ring of Matrices 466--468
V. E. Hoggatt, Jr. and
Marjorie Bicknell Special Determinants Found within
Generalized Pascal Triangles . . . . . . 469--479
L. C. Hsu Note on a Combinatorial Algebraic
Identity and its Application . . . . . . 480--484
Joseph Arkin A Solution to the Classical Problem of
Finding Systems of Three Mutually
Orthogonal Numbers in a Cube Formed by
Three Superimposed $ 10 \times 10 \times
10 $ Cubes . . . . . . . . . . . . . . . 485--489
W. A. Sentance A Further Analysis of Benford's Law . . 490--494
Michael F. Lynch A Fibonacci-Related Series in an Aspect
of Information Retrieval . . . . . . . . 495--499
Anonymous Letter to the Editor . . . . . . . . . . 500
Raymond E. Whitney Advanced Problems and Solutions . . . . 501--507
Dale D. Shea On the Number of Divisions Needed in
Finding the Greatest Common Divisor . . 508--510
Marjorie Bicknell A Primer for the Fibonacci Numbers: Part
XIII . . . . . . . . . . . . . . . . . . 511--516
Harold D. Shane A Fibonacci Probability Function . . . . 517--522
Frank J. D. Trumper Some General Fibonacci Shift Formulae 523
Anonymous Errata . . . . . . . . . . . . . . . . . 524
Carl F. Moore More Hidden Hexagon Squares . . . . . . 525
J. Wlodarski The Balmer Series and the Fibonacci
Numbers . . . . . . . . . . . . . . . . 526
Bruce W. King A Polynomial with Generalized Fibonacci
Coefficients . . . . . . . . . . . . . . 527--532
Furio Alberti Another Proof for a Continued Fraction
Identity . . . . . . . . . . . . . . . . 533--534
Daniel Lance Herrick On the Periodicity of the Terminal
Digits in Fibonacci Sequences . . . . . 535--538
Charles W. Trigg Geometric Proof of a Result of Lehmer's 539--540
Walter W. Horner Fibonacci and Apollonius . . . . . . . . 541--542
Jerome Rothstein A Method for Constructing Singly Even
Magic Squares . . . . . . . . . . . . . 543--544
William L. Mathis The $Z$ Transform and the Fibonacci
Sequence . . . . . . . . . . . . . . . . 545--546
M. N. S. Swamy On Generalized Fibonacci Quaternions . . 547--549
A. P. Hillman Elementary Problems and Solutions . . . 550--553
Anonymous Volume Index . . . . . . . . . . . . . . 554
L. Carlitz Fibonacci Notes --- 1. Zero-One
Sequences and Fibonacci Numbers of
Higher Order . . . . . . . . . . . . . . 1--10
Brother L. Raphael Linearly Recursive Sequences of Integers 11--37
H. E. Huntley The Golden Ellipse . . . . . . . . . . . 38--40
R. R. Laxton On a Problem of M. Ward . . . . . . . . 41--44
A. K. Gupta Generalized Hidden Hexagon Squares . . . 45
Donald E. Knuth Letter to the Editor . . . . . . . . . . 46, 79, 82
V. E. Hoggatt, Jr. and
Marjorie Bicknell Diagonal Sums of the Trinomial Triangle 47--50
Agnes Andreassian Fibonacci Sequences Modulo $m$ . . . . . 51--64
H. E. Huntley Phi: Another Hiding Place . . . . . . . 65
Anonymous Fibonacci Association Meeting: Program 66
D. V. Jaiswal Some Geometrical Properties of the
Generalized Fibonacci Sequences . . . . 67--70
Calvin T. Long and
V. E. Hoggatt, Jr. Sets of Binomial Coefficients with Equal
Products . . . . . . . . . . . . . . . . 71--79
V. C. Harris On Daykin's Algorithm for Finding the G.
C. D. . . . . . . . . . . . . . . . . . 80
Sahib Singh Stufe of a Finite Field . . . . . . . . 81--82
Edgar Karst Iteration Algorithms for Certain Sums of
Squares . . . . . . . . . . . . . . . . 83--86
Michael R. Turner Certain Congruence Properties (Modulo
100) of Fibonacci Numbers . . . . . . . 87--91
Santosh Kumar Fibonaccian Pathological Curves . . . . 92--94
G. E. Bergum and
V. E. Hoggatt, Jr. Irreducibility of Lucas and Generalized
Lucas Polynomials . . . . . . . . . . . 95--100
A. P. Hillman Elementary Problems and Solutions . . . 101--106
R. E. Whitney Advanced Problems and Solutions . . . . 107--112
Verner E. Hoggatt, Jr. and
Calvin T. Long Divisibility Properties of Generalized
Fibonacci Polynomials . . . . . . . . . 113--120
Carl Serkland Generating Identities for Pell Triples 121--128
G. L. Alexanderson and
L. F. Klosinski A Fibonacci Analogue of Gaussian
Binomial Coefficients . . . . . . . . . 129--132
Joseph Arkin A Solution of Orthogonal Triples in Four
$ 10 \times 10 \times 10 $ Superimposed
Latin Cubes . . . . . . . . . . . . . . 133--140
George E. Andrews Combinatorial Analysis and Fibonacci
Numbers . . . . . . . . . . . . . . . . 141--145
Brother Alfred Brousseau Fibonacci Summations Involving a Power
of a Rational Number --- Summary . . . . 146
V. E. Hoggatt, Jr. and
Marjorie Bicknell A Primer for the Fibonacci Numbers: Part
XIV . . . . . . . . . . . . . . . . . . 147--156
Henry W. Gould Generalization of Hermite's Divisibility
Theorems and the Mann--Shanks Primality
Criterion for $s$-Fibonomial Arrays . . 157--166
Brother Alfred Brousseau Algorithms for Third-Order Recursion
Sequences . . . . . . . . . . . . . . . 167--174
Paul A. Catlin On the Divisors of Second-Order
Recurrences . . . . . . . . . . . . . . 175--178
L. Carlitz Fibonacci Notes --- 2. Multiple
Generating Functions . . . . . . . . . . 179--185
Marcia Ascher A Combinatorial Identity . . . . . . . . 186--188
V. E. Hoggatt, Jr. and
Gerald E. Bergum Divisibility and Congruence Relations 189--195
Myron Tepper Combinations and Sums of Powers . . . . 196--198
Barry Brent Functional Equations with Prime Roots
from Arithmetic Expressions for $
G_\alpha $ . . . . . . . . . . . . . . . 199--207
Barry Brent An Expansion of $ e^x $ off Roots of One 208
Charles W. Trigg Infinite Sequences of Palindromic
Triangular Numbers . . . . . . . . . . . 209--211
Gerald E. Bergum A Note on the Fermat--Pellian Equation 212
Raymond E. Whitney Advanced Problems and Solutions . . . . 213--219
A. P. Hillman Elementary Problems and Solutions . . . 220
V. E. Hoggatt, Jr. and
Marjorie Bicknell Triangular Numbers . . . . . . . . . . . 221--230
A. J. W. Hilton On Fern's Theorem on the Expansion of
Fibonacci and Lucas Numbers . . . . . . 231
Anonymous The Fibonacci Association Research
Conference . . . . . . . . . . . . . . . 232
F. J. Wunderlich and
D. E. Shaw and
M. J. Hones Argand Diagrams of Extended Fibonacci
and Lucas Numbers . . . . . . . . . . . 233--234
Duane W. DeTemple A Pentagonal Arch . . . . . . . . . . . 235--236
A. G. Shannon A Generalization of the Hilton--Fern
Theorem on the Expansion of Fibonacci
and Lucas Numbers . . . . . . . . . . . 237--240
J. W. Walton and
A. F. Horadam Some Aspects of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 241--250
P. J. deBruijn An Extension of Fibonacci's Sequence . . 251--258
A. J. W. Hilton Spanning Trees and Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 259--262
D. V. Jaiswal On Polynomials Related to Tchebichef
Polynomials of the Second Kind . . . . . 263--264
L. Carlitz and
Margaret Hodel Corrigendum to: ``Enumeration of
Two-Line Arrays'' . . . . . . . . . . . 265--266
A. F. Horadam Oresme Numbers . . . . . . . . . . . . . 267--270
Daniel Shanks Incredible Identities . . . . . . . . . 271
J. E. Walton and
A. F. Horadam Some Further Identities for the
Generalized Fibonacci Sequence $ H_n $ 272--280
A. G. Shannon Explicit Expressions for Powers of
Linear Recursive Sequences . . . . . . . 281--287
Joseph Arkin and
E. G. Straus Latin $k$-Cubes . . . . . . . . . . . . 288--291
M. G. Monzingo On Extending the Fibonacci Numbers to
the Negative Integers . . . . . . . . . 292
A. G. Shannon A Method of Carlitz Applied to the $k$
th Power Generating Function for
Fibonacci Numbers . . . . . . . . . . . 293--298
Richard Guy and
Daniel Shanks A Constructed Solution of $ \sigma (n) =
\sigma (n + 1) $ . . . . . . . . . . . . 299
H. W. Gould The Design of the Four Binomial
Identities: Moriarty Intervenes . . . . 300--308
Raymond E. Whitney Advanced Problems and Solutions . . . . 309--312
A. P. Hillman Elementary Problems and Solutions . . . 313--316
L. Carlitz Fibonacci Notes --- 3: $q$-Fibonacci
Numbers . . . . . . . . . . . . . . . . 317--322
Warren Page P.Q.M.-Cycles, a Generalized Number
Problem . . . . . . . . . . . . . . . . 323--325
Charles W. Trigg The Apollonius Problem . . . . . . . . . 326
A. G. Shannon Some Properties of a Fundamental
Recursive Sequence of Arbitrary Order 327--334
Paul Erd\Hos Letter to the Editor . . . . . . . . . . 335
C. A. Church, Jr. Lattice Paths and Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 336--338
A. J. W. Hilton On the Partition of Haradam's
Generalized Sequences into Generalized
Fibonacci and Generalized Lucas
Sequences . . . . . . . . . . . . . . . 339--344
Anonymous Errata . . . . . . . . . . . . . . . . . 345
I. J. Good A Reciprocal Series of Fibonacci Numbers 346
Norris Goodwin Power Series and Cyclic Decimals . . . . 347
A. F. Horadam On Generating Functions for Powers of a
Generalized Sequence of Numbers . . . . 348
Paul A. Catlin A Lower Bound for the Period of the
Fibonacci Series Modulo $M$ . . . . . . 349--350
A. G. Shannon and
A. F. Horadam and
S. N. Collings Some Congruences for Fibonacci Numbers 351--354
Daniel C. Fielder Fibonacci Numbers in Tree Counts for
Sector and Related Graphs . . . . . . . 355--359
M. J. Hodel Combinatorial Interpretation of an
Analog of Generalized Binomial
Coefficients . . . . . . . . . . . . . . 360--362
Murray Hochberg On the Set of Divisor of a Number . . . 363--364
Paul A. Catlin On the Multiplication of Recurrences . . 365--367
David Zeitlin A Note on Fermat's Last Theorem . . . . 368
L. Carlitz A $q$-Identity . . . . . . . . . . . . . 369--372
R. C. Grimson The Evaluation of Certain Arithmetic
Sums . . . . . . . . . . . . . . . . . . 373--380
Marcellus E. Waddill Matrices and Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 381--386
Charles W. Trigg Antimagic Squares Derived from the
Third-Order Magic Square . . . . . . . . 387--390
Emanuel Vegh Concerning an Equivalence Relation for
Matrices . . . . . . . . . . . . . . . . 391--392
H. W. Gould Some Sequences Generated by Spiral
Sieving Methods . . . . . . . . . . . . 393--397
Raymond E. Whitney Advanced Problems and Solutions . . . . 398--402
A. P. Hillman Elementary Problems and Solutions . . . 403--406
Anonymous Volume Index . . . . . . . . . . . . . . 407
Krishnaswami Alladi A Farey Sequence of Fibonacci Numbers 1--10
I. J. Good The Number of Orderings of $n$
Candidates When Ties are Permitted . . . 11--18
G. E. Bergum and
W. J. Wagner and
V. E. Hoggatt, Jr. Chebyshev Polynomials and Related
Sequences . . . . . . . . . . . . . . . 19--24
W. L. McDaniel and
Peter Hagis, Jr. Some Results Concerning the
Non-Existence of Odd Perfect Numbers of
the Form $ p^\alpha M^{2 \beta } $ . . . 25--28
Joseph J. Heed and
Lucille Kelly An Interesting Sequence of Fibonacci
Sequence Generators . . . . . . . . . . 29--30
Krishnaswami Alladi A Rapid Method to Form Farey Fibonacci
Fractions . . . . . . . . . . . . . . . 31
Jeffrey Shallit A Simple Proof that Phi is Irrational 32
Brother Alfred Brousseau Symmetric Sequences . . . . . . . . . . 33--41
John W. Layman Some Interesting Necessary Conditions
for $ (a - 1)^n + (b - 1)^n - (c - 1)^n
= 0 $ . . . . . . . . . . . . . . . . . 42--44
Herbert L. Holden Fibonacci Tiles . . . . . . . . . . . . 45--49
Hugo S. Sun Embedding a Semigroup in a Ring . . . . 50
Kenneth R. Rebman The Sequence: $ 1 5 16 45 121 320 $ ---
In Combinatorics . . . . . . . . . . . . 51--55
Norman Woo Non-Basic Triples . . . . . . . . . . . 56--58
Paul F. Byrd New Relations Between Fibonacci and
Bernoulli Numbers . . . . . . . . . . . 59--69
Sin Hitotumatu and
Daihachiro Sato Star of David Theorem (I) . . . . . . . 70
L. Carlitz and
Richard Scoville Eulerian Numbers and Operators . . . . . 71--83
James P. Jones Diophantine Representation of the
Fibonacci Numbers . . . . . . . . . . . 84--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--93
A. P. Hillman Elementary Problems and Solutions . . . 94--96
L. Carlitz Fibonacci Notes --- 4: $q$-Fibonacci
Polynomials . . . . . . . . . . . . . . 97--102
Paul S. Bruckman A General Identity for Multisecting
Generating Functions . . . . . . . . . . 103--104
Paul S. Bruckman A Formula for $ A_n^2 (x) $ . . . . . . 105--106
Joseph Arkin and
V. E. Hoggatt, Jr. The Generalized Fibonacci Number and Its
Relation to Wilson's Theorem . . . . . . 107--109
Delano P. Wegener and
Joseph A. Wehlen Pythagorean Triangles --- Abstract . . . 110
Paul F. Byrd Relations Between Euler and Lucas
Numbers . . . . . . . . . . . . . . . . 111--114
G. E. Bergum and
V. E. Hoggatt, Jr. Sums and Products for Recurring
Sequences . . . . . . . . . . . . . . . 115--120
L. Carlitz Some Identities of Bruckman . . . . . . 121--126
Henry W. Gould Formal Proof of Equivalence of Two
Solutions of the General Pascal
Recurrence . . . . . . . . . . . . . . . 127--128
L. Carlitz Note on Some Generating Functions . . . 129--133
C. K. Wong and
T. W. Maddocks A Generalized Pascal's Triangle . . . . 134--136
V. E. Hoggatt, Jr. and
Krishnaswami Alladi Generalized Fibonacci Tiling . . . . . . 137--144
Brother Alfred Brousseau A Least Integer Sequence Investigation 145--146
H. L. Alder and
Amin A. Muwafi Identities Relating the Number of
Partitions into an Even and Odd Number
of Parts . . . . . . . . . . . . . . . . 147--149
D. H. Lehmer Fibonacci and Related Sequences in
Periodic Tridiagonal Matrices . . . . . 150--158
H. J. A. Sallé A Maximum Value for the Rank of
Apparition of Integers in Recursive
Sequences . . . . . . . . . . . . . . . 159--160
V. E. Hoggatt, Jr. and
John W. Phillips Fibonacci and Lucas Sums in the
$r$-Normal Triangle --- Abstract . . . . 161
Sam Lindle Exponential Modular Identity Elements
and the Generalized Last Digit Problem 162--170
Alexander G. Abercrombie Letter to the Editor . . . . . . . . . . 171--173
James M. Mann Signed $b$-Adic Partitions . . . . . . . 174--180
Ada Booth Idiot's Roulette Revisited . . . . . . . 181--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--189
A. P. Hillman Elementary Problems and Solutions . . . 190--192
V. E. Hoggatt, Jr. and
G. E. Bergum Generalized Convolution Arrays . . . . . 193--197
Anonymous Letter to the Editor . . . . . . . . . . 198
Michael D. Miller A Recursively Defined Divisor Function 199--203
William Raymond Griffin Significance of Even-Oddness of a
Prime's Penultimate Digit . . . . . . . 204
H. S. Hahn Another Property of Magic Squares . . . 205--208
M. W. Bunder On Halsey's Fibonacci Function . . . . . 209--210
Donald C. Cross Fibonacci Multi-Multigrades . . . . . . 211--212
H. C. Williams On Fibonacci Numbers of the Form $ k^2 +
1 $ . . . . . . . . . . . . . . . . . . 213--214
Richard P. Stanley The Fibonacci Lattice . . . . . . . . . 215--232
Krishnaswami Alladi and
V. E. Hoggatt, Jr. Compositions with Ones and Twos . . . . 233--239
H. C. Williams The Rank of Apparition of a Generalized
Fibonacci Sequences . . . . . . . . . . 240--242
Brian Peterson and
V. E. Hoggatt, Jr. On the Solutions to the Diophantine
Equation $ x^2 + x y - y^2 = \pm D $, or
the Number of Fibonacci-Type Sequences
with a Given Characteristic . . . . . . 243--251
Abbe Mowshowitz and
Frank Harary Enumeration of End-Labeled Trees . . . . 252--254
Krishnaswami Alladi Approximation of Irrationals with Farey
Fibonacci Fractions . . . . . . . . . . 255--259
C. J. Everett A Greatest Integer Theorem for Fibonacci
Spaces . . . . . . . . . . . . . . . . . 260--262
Delano P. Wegener Primitive Pythagorean Triples with Sum
of Difference of Legs Equal to a Prime 263--277
V. E. Hoggatt, Jr. and
Marjorie Bicknell Special Partitions . . . . . . . . . . . 278
M. W. Bunder Products and Powers . . . . . . . . . . 279
M. W. Bunder A Special Case of the Generalized
Fibonacci Sequence Over an Arbitrary
Ring with Identity . . . . . . . . . . . 280
Raymond E. Whitney Advanced Problems and Solutions . . . . 281--284
A. P. Hillman Elementary Problems and Solutions . . . 285--288
Richard R. Stone General Identities for Fibonacci and
Lucas Numbers with Polynomial Subscripts
in Several Variables . . . . . . . . . . 289--294
David Singmaster Repeated Binomial Coefficients and
Fibonacci Numbers . . . . . . . . . . . 295--298
J. L. Brown, Jr. A Recursive Method for Counting Integers
not Representable in Certain Expansions 299--302
L. Carlitz and
Richard Scoville A Note on Weighted Sequences . . . . . . 303--306
C. Ryavec An Application of Spectral Theory to
Fibonacci Numbers . . . . . . . . . . . 307--308
Gregory Wulczyn Minimum Solutions to $ x^2 - D y^2 = \pm
1 $ . . . . . . . . . . . . . . . . . . 309--311
N. Georgieva Distribution of the Zeroes of One Class
of Polynomials . . . . . . . . . . . . . 312--314
Andras Recski On the Generalization of the Fibonacci
Numbers . . . . . . . . . . . . . . . . 315--317
Larry Taylor The General Law of Quadratic Reciprocity 318
Daniel Shanks Non-Hypotenuse Numbers . . . . . . . . . 319--321
Lawrence Somer The Fibonacci Ratios $ F_{k + 1} / F_k $
Modulo $p$ . . . . . . . . . . . . . . . 322--324
S. M. Tanny On Alternating Subsets of Integers . . . 325--328
Hugo S. Sun Structure of the Reduced Residue System
with Composite Modulus . . . . . . . . . 329--330
J. L. Hunsucker and
Carl Pomerance On an Interesting Property of
11234955056179752809 . . . . . . . . . . 331--333
William Webb Distribution of the First Digits of
Fibonacci Numbers . . . . . . . . . . . 334--336
Henry L. Alder and
Amin A. Muwafi Generalizations of Euler's Recurrence
Formula for Partitions . . . . . . . . . 337--339
Raphael Finkelstein On Lucas Numbers which are One More than
a Square . . . . . . . . . . . . . . . . 340--342
George Berzsenyi Sums of Products of Generalized
Fibonacci Numbers . . . . . . . . . . . 343--344
Marjorie Bicknell A Primer on the Pell Sequence and
Related Sequences . . . . . . . . . . . 345--349
V. E. Hoggatt, Jr. and
Marjorie Bicknell Palindromic Compositions . . . . . . . . 350--355
A. R. Mitchell and
R. W. Mitchell A Note on Topologies on Finite Sets . . 356
V. E. Hoggatt, Jr. and
Paul S. Bruckman The $H$-Convolution Transform . . . . . 357--368
Raymond E. Whitney Advanced Problems and Solutions . . . . 369--372
A. P. Hillman Elementary Problems and Solutions . . . 373--377
Anonymous Volume Index . . . . . . . . . . . . . . 378
Humphrey Nash Some Operational Formulas . . . . . . . 1--8
P. Monteiro and
R. W. Newcomb Minimal and Maximal Fibonacci
Representations: Boolean Generation . . 9--11
Anonymous Letter to the Editor . . . . . . . . . . 12
Basil Davis Some Remarks on Initial Digits . . . . . 13--14
Samuel T. Stern On Isomorphisms Between the Naturals and
Integers . . . . . . . . . . . . . . . . 15--16
Leon Bankoff A Fibonacci Curiosity . . . . . . . . . 17
Gregory Wulczyn On Continued Fraction Expansions Whose
Elements are All Ones . . . . . . . . . 18--22
M. G. Monzingo On Congruences Modulo a Power of a Prime 23
Donald Cross A More General Fibonacci Multigrade . . 24
L. G. Zukerman Fibonacci Ratio in Electric Wave Filters 25--26
Michael Willett On a Theorem of Kronecker . . . . . . . 27--28
Leon Bankoff A Fibonacci Pleasantry . . . . . . . . . 29
Dean B. Priest and
Stephen W. Smith Column Generators for Coefficients of
Fibonacci and Fibonacci-Related
Polynomials . . . . . . . . . . . . . . 30--34
Theodore J. Cullen A Summation Identity . . . . . . . . . . 35--36
T. G. Lewis and
B. J. Smith and
M. Z. Smith Fibonacci Sequences and Memory
Management . . . . . . . . . . . . . . . 37--41
N. C. Mohanty Interesting Properties of Laguerre
Polynomials . . . . . . . . . . . . . . 42
G. E. Bergum and
V. E. Hoggatt, Jr. Numerator Polynomial Coefficient Array
for the Convolved Fibonacci Sequence . . 43--47
Anonymous Letter to the Editor . . . . . . . . . . 48
Haim Hanani A Combinatorial Identity . . . . . . . . 49--51
T. E. Stanley Some Remarks on the Periodicity of the
Sequence of Fibonacci Numbers . . . . . 52--53
S. H. L. Kung Parity Triangles of Pascal's Triangle 54
L. Carlitz The Saalschützian Theorems . . . . . . . 55--63
Robert W. Stringall A Density Relationship Between $ a x + b
$ and $ [x / c] $ . . . . . . . . . . . 64--66
E. A. Enneking and
J. C. Ahuja Generalized Bell Numbers . . . . . . . . 67--73
T. K. Puttaswamy A Note on a Theorem of W. B. Ford . . . 74
George H. Weiss and
Menachem Dishon A Method for the Evaluation of Certain
Sums Involving Binomial Coefficients . . 75--77
Robert Gordon Babb II On the Order of Systems of Two
Simultaneous Linear Difference Equations
in Two Variables . . . . . . . . . . . . 78--82
J. E. Walton Lucas Polynomials and Certain Circular
Functions of Matrices . . . . . . . . . 83--87
Raymond E. Whitney Advanced Problems and Solutions . . . . 88--92
A. P. Hillman Elementary Problems and Solutions . . . 93--96
Partha Pratim Majumder and
Aravinda Chakravati Variation in the Number of Ray- and
Disc-Florets in Four Species of
Compositae . . . . . . . . . . . . . . . 97--100
S. Tauber Combinatorial Numbers in $ C^n $ . . . . 101--110
David T. Walker Consecutive Integer Pairs of Powerful
Numbers and Related Diophantine
Equations . . . . . . . . . . . . . . . 111--116
V. E. Hoggatt, Jr. and
G. L. Alexanderson Sums of Partition Sets in Generalized
Pascal Triangles I . . . . . . . . . . . 117--125
Hugo Norden Per Nòrgård's ``Canon'' . . . . . . . . . 126--128
W. Elliott Greig Bode's Rule and Folded Sequences . . . . 129--133
James P. Jones Diophantine Representation of the Lucas
Numbers . . . . . . . . . . . . . . . . 134
V. E. Hoggatt, Jr. and
Marjorie Bicknell Pascal, Catalan, and General Sequence
Convolution Arrays in a Matrix . . . . . 135--142
H. W. Gould Letter to the Editor . . . . . . . . . . 143
V. E. Hoggatt, Jr. and
Krishnaswami Alladi In-Winding Spirals . . . . . . . . . . . 144--146
James Alonso Arithmetic Sequences of Higher Order . . 147--152
Ronald Solomon Divisibility Properties of Certain
Recurring Sequences . . . . . . . . . . 153--158
Brother Alfred Brousseau Recursion Relations of Products of
Linear Recursion Sequences . . . . . . . 159--166
Joseph Arkin and
Paul Smith Trebly-Magic Systems in a Latin $3$-Cube
of Order Eight . . . . . . . . . . . . . 167--170
P. C. Consul Some Factorable Determinants . . . . . . 171--172
Haruo Hosoya Fibonacci Triangle . . . . . . . . . . . 173--179
Larry Taylor A Conjecture Relating Quartic
Reciprocity and Quartic Residuacity to
Primitive Pythagorean Triples . . . . . 180--181
Raymond E. Whitney Advanced Problems and Solutions . . . . 182--187
A. P. Hillman Elementary Problems and Solutions . . . 188--192
P. S. Bruckman and
I. J. Good A Generalization of a Series of DeMorgan
with Applications of Fibonacci Type . . 193--195
G. J. Rieger On the Harris Modification of the
Euclidean Algorithm . . . . . . . . . . 196--196
David G. Beverage Polynomials $ P_{2 n + 1}(x) $
Satisfying $ P_{2 n + 1}(F_k) = F_{(2 n
+ 1)k} $ . . . . . . . . . . . . . . . . 197--200
Louis Shapiro Fibonacci Numbers and Upper Triangular
Groups . . . . . . . . . . . . . . . . . 201--202
David Lee Hilliker On the Infinite Multinomial Expansion 203--205
R. B. Killgrove The Sum of Two Powers is a Third,
Sometimes . . . . . . . . . . . . . . . 206--209
Donald W. Robinson The Rank and Period of a Linear
Recurrent Sequence Over a Ring . . . . . 210--213
L. Kuipers Letter to the Editor . . . . . . . . . . 214
F. P. Sayer The Sums of Certain Series Containing
Hyperbolic Functions . . . . . . . . . . 215--223
V. E. Hoggatt, Jr. and
Marjorie Bicknell Sequences of Matrix Inverses from
Pascal, Catalan, and Related Convolution
Arrays . . . . . . . . . . . . . . . . . 224--232
Helaman Rolfe Pratt Ferguson On a Generalization of the Fibonacci
Numbers Useful in Memory Allocation
Schema; or All About the Zeroes of $ Z^k
- Z^{k - 1} - 1, k > 0 $ . . . . . . . . 233--243
Theresa P. Vaughan A Note on Some Arithmetic Functions
Connected with the Fibonacci Numbers . . 244--248
L. Carlitz Some Binomial Sums . . . . . . . . . . . 249--253
L. Carlitz Restricted Compositions . . . . . . . . 254--264
Myron Tepper Sums of Combination Products . . . . . . 265--271
V. E. Hoggatt, Jr. and
Marjorie Bicknell A Primer for the Fibonacci Numbers, Part
XV: Variations on Summing a Series of
Reciprocals of Fibonacci Numbers . . . . 272--276
David A. Klarner A Model for Population Growth . . . . . 277--281
Raymond E. Whitney Advanced Problems and Solutions . . . . 282--285
A. P. Hillman Elementary Problems and Solutions . . . 286--288
Robert Silber and
Ralph Gellar The Algebra of Fibonacci Representations 289--326
L. Carlitz Set Partitions . . . . . . . . . . . . . 327--342
Claudia Smith and
Verner E. Hoggatt, Jr. Primitive Periods of Generalized
Fibonacci Sequences . . . . . . . . . . 343--347
P. Erd\Hos and
R. L. Graham On the Prime Factors of \binom(n,k) . . 348--352
R. B. McQuistan Mixed Nearest Neighbor Degeneracy for
Particles on a One-Dimensional Lattice
Space . . . . . . . . . . . . . . . . . 353--357
Leon Bernstein A Formula for Fibonacci Numbers From a
New Approach to Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 358--367
Anonymous Letter to the Editor . . . . . . . . . . 368
Clark Kimberling Divisibility Properties of Recurrent
Sequences . . . . . . . . . . . . . . . 369--376
Kurt Fischer The Fibonacci Sequence Encountered in
Nerve Physiology . . . . . . . . . . . . 377--379
Robert Silber A Fibonacci Property of Wythoff Pairs 380--384
M. L. Glasser and
M. S. Klamkin On Some Inverse Tangent Summations . . . 385--387
M. C. Monzingo A Note on the Golden Ellipse . . . . . . 388
Hansraj Gupta A Direct Method of Obtaining
Farey--Fibonacci Sequences . . . . . . . 389--390
M. G. Monzingo On Consecutive Primitive Roots . . . . . 391
David Lee Hilliker On the Infinite Multinomial Expansion,
II . . . . . . . . . . . . . . . . . . . 392--394
V. E. Hoggatt, Jr. and
Marjorie Bicknell Catalan and Related Sequences Arising
from Inverses of Pascal's Triangle
Matrices . . . . . . . . . . . . . . . . 395--404
Bro. Basil Davis and
V. E. Hoggatt, Jr. Exponentials and Bessel Functions . . . 405, 418, 426
Helene Hedian The Golden Section and the Artist . . . 406--418
Joseph Ercolano Golden Sequences of Matrices with
Application to Fibonacci Algebra . . . . 419--426
L. Carlitz Some Sums of Multinomial Coefficients 427--438
Morton Abramson Restricted Combinations and Compositions 439--451
Bob Jones Ode to Pascal's Triangle . . . . . . . . 452
V. E. Hoggatt, Jr. and
Marjorie Bicknell A Reciprocal Series of Fibonacci Numbers
with Subscripts $ 2^n k $ . . . . . . . 453--454
Verner E. Hoggatt, Jr. Response . . . . . . . . . . . . . . . . 455
M. J. DeLeon Pell's Equation and Pell Number Triples 456--460
Krishnaswami Alladi On Polynomials Generated by Triangular
Arrays . . . . . . . . . . . . . . . . . 461--465
Raymond E. Whitney Advanced Problems and Solutions . . . . 466--469
A. P. Hillman Elementary Problems and Solutions . . . 470--473
Anonymous Volume Index . . . . . . . . . . . . . . 474
C. C. Yalavigi Residues of Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 1
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Composites and Primes Among Powers of
Fibonacci Numbers, Increased or
Decreased by One . . . . . . . . . . . . 2
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Divisibility by Fibonacci and Lucas
Squares . . . . . . . . . . . . . . . . 3--7
John W. Jameson Letter to the Editor . . . . . . . . . . 8
J. Spencer An Elementary Proof of Kronecker's
Theorem . . . . . . . . . . . . . . . . 9--10
Peter J. Slater Fibonacci Numbers in the Count of
Spanning Trees . . . . . . . . . . . . . 11--13
W. R. Utz The Diophantine Equation $ (x_1 + x_2 +
\cdots {} + x_n)^2 = x^3_1 + x^3_2 +
\cdots {} + x^3_n $ . . . . . . . . . . 14
Maurice Mignotte An Application of W. Schmidt's Theorem
Transcendental Numbers and Golden Number 15--16
W. E. Greig The Reciprocal Period Law . . . . . . . 17--20
A. K. Whitford Binet's Formula Generalized . . . . . . 21
David Lee Hilliker On the Multinomial Theorem . . . . . . . 22--24
H. W. Gould A Fibonacci Formula of Lucas and its
Subsequent Manifestations and
Rediscoveries . . . . . . . . . . . . . 25--29
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Numerator Polynomial Coefficient Arrays
for Catalan and Related Sequence
Convolution Triangles . . . . . . . . . 30--34
Lawrence Somer Fibonacci-Like Groups and Periods of
Fibonacci-Like Sequences . . . . . . . . 35--40
Douglas A. Fults Solution of a Certain Recurrence
Relation . . . . . . . . . . . . . . . . 41
Krishnaswami Alladi and
V. E. Hoggatt, Jr. On Tribonacci Numbers and Related
Functions . . . . . . . . . . . . . . . 42--45
W. E. Greig Sums of Fibonacci Reciprocals . . . . . 46--48
L. Carlitz Fibonacci Notes --- 5. Zero-One
Sequences Again . . . . . . . . . . . . 49--56
Robert Silber On the $N$-Canonical Fibonacci
Representations of Order $N$ . . . . . . 57--66
H. W. Gould A Rearrangement of Series Based on a
Partition of the Natural Numbers . . . . 67--72
M. N. S. Swamy A Formula for $ \sum_1^n F_k(x) y^{n -
k} $ and its Generalization to
$r$-bonacci Polynomials . . . . . . . . 73--77
L. Carlitz Some Sums Containing the Greatest
Integer Function . . . . . . . . . . . . 78--84
Robert Silber Wythoff's Nim and Fibonacci
Representations . . . . . . . . . . . . 85--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--92
A. P. Hillman Elementary Problems and Solutions . . . 93--96
H. C. Williams Properties of Some Functions Similar to
Lucas Functions . . . . . . . . . . . . 97--111
Harvey J. Hinden Phi Again: a Relationship Between the
Golden Ratio and the Limit of a Ratio of
Modified Bessel Functions . . . . . . . 112, 152
Gerald E. Bergum and
Verner E. Hoggatt, Jr. Limits of Quotients for the Convolved
Fibonacci Sequence and Related Sequences 113--115
B. J. Cerimele Summation of Multiparameter Harmonic
Series . . . . . . . . . . . . . . . . . 116, 144, 149, 172
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Fibonacci Convolution Sequences . . . . 117--121
E. A. Parberry Two Recursion Relations for $ F(F(n)) $ 122
Donald B. Small A Matrix Sequence Associated with a
Continued Fraction Expansion of a Number 123--130
Verner E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Generalized Lucas Sequences . . . . . . 131--139
Stanley Bezuszka and
Lou D'Angelo An Application of Tribonacci Numbers . . 140--144
Joseph Mandelson Amateur Interests in the Fibonacci
Series IV Calculation of Group Sizes of
Residues of Moduli . . . . . . . . . . . 145--149
C. C. Yalavigi and
H. V. Krishna Periodic Lengths of the Generalized
Fibonacci Sequence Modulo $p$ . . . . . 150--152
Krishnaswami Alladi and
A. G. Shannon On a Property of Consecutive
Farey--Fibonacci Fractions . . . . . . . 153--154
Doron Zeilberger Sums of Products Involving Fibonacci
Sequences . . . . . . . . . . . . . . . 155
Walter Gerdes Convergent Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 156--160
O. R. Ainsworth On Generating Functions . . . . . . . . 161--163
K. Joseph Davis A Result in Analytic Number Theory . . . 164--165
V. E. Hoggatt, Jr. Additive Partition I . . . . . . . . . . 166
Barry Powell Proof of a Special Case of Dirichlet's
Theorem . . . . . . . . . . . . . . . . 167--169
Ronald Evans Diophantine Equations Involving the
Greatest Integer Function . . . . . . . 170--172
Avery A. Morton The Fibonacci Series and the Periodic
Table of Elements . . . . . . . . . . . 173--175
W. E. Greig On Fibonacci and Triangular Numbers . . 176--177
Chi-Leung Lau The Periodic Generating Sequence . . . . 178--181
V. E. Hoggatt, Jr. Additive Partition II . . . . . . . . . 182
Denton Hewgill A Relationship Between Pascal's Triangle
and Fermat's Numbers . . . . . . . . . . 183--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--188
A. P. Hillman Elementary Problems and Solutions . . . 189--192
April Scott and
Tom Delaney and
V. E. Hoggatt, Jr. The Tribonacci Sequence . . . . . . . . 193--200
W. Fred Lunnon The Pascal Matrix . . . . . . . . . . . 201--204
C. J. Park Zero-One Sequences and Stirling Numbers
of the Second Kind . . . . . . . . . . . 205--206
W. D. Spears and
T. F. Higginbotham On Powers of the Golden Ratio . . . . . 207--208
Stephan R. Cavior Uniform Distribution for Prescribed
Moduli . . . . . . . . . . . . . . . . . 209--210
V. E. Hoggatt, Jr. and
Krishnaswami Alladi Limiting Ratios of Convolved Recursive
Sequences . . . . . . . . . . . . . . . 211--214
G. E. Bergum and
V. E. Hoggatt, Jr. An Application of the Characteristic of
the Generalized Fibonacci Sequence . . . 215--219
H. D. Allen Metric Paper to Fall Short of ``Golden
Mean'' . . . . . . . . . . . . . . . . . 220
Blagoj S. Popov Generating Functions for Powers of
Certain Second-Order Recurrence
Sequences . . . . . . . . . . . . . . . 221--223
Kenneth B. Stolarsky A Set of Generalized Fibonacci Sequences
Such That Each Natural Number Belongs to
Exactly One . . . . . . . . . . . . . . 224
V. E. Hoggatt, Jr. and
Paul S. Bruckman Periodic Continued Fraction
Representations of Fibonacci-Type
Irrationals . . . . . . . . . . . . . . 225--229
Paul S. Bruckman Pi-Oh-MY! . . . . . . . . . . . . . . . 230
C. J. Park Zero-One Sequences and Stirling Numbers
of the First Kind . . . . . . . . . . . 231
Guy A. R. Guillot Problems . . . . . . . . . . . . . . . . 232
George Berzsenyi Gaussian Fibonacci Numbers . . . . . . . 233--235
Paul S. Bruckman Constantly Mean . . . . . . . . . . . . 236
M. Deza On Minimal Number of Terms in
Representation of Natural Numbers as a
Sum of Fibonacci Numbers . . . . . . . . 237
D. Beverage Letter to the Editor . . . . . . . . . . 238
V. E. Hoggatt, Jr. and
Krishnaswami Alladi Compositions and Recurrence Relations II 239--244
Ethan D. Bolker A Topological Proof of a Well-Known Fact
about Fibonacci Numbers . . . . . . . . 245
L. Carlitz and
Richard Scoville Zero-One Sequences and Fibonacci Numbers 246--253
Guy A. R. Guillot The Unified Number Theory . . . . . . . 254
A. F. Horadam Polynomials Associated with Chebyshev
Polynomials of the First Kind . . . . . 255--257
Delano P. Wegener Semi-Associates in $ Z[\sqrt {2}] $ and
Primitive Pythagorean Triples . . . . . 258--264
Stephan R. Cavior Uniform Distribution $ \pmod {m} $ of
Recurrent Sequences . . . . . . . . . . 265--267
A. G. Shannon Tribonacci Numbers and Pascal's Pyramid 268
Paul S. Bruckman On Generating Functions with Composite
Coefficients . . . . . . . . . . . . . . 269--275
L. Carlitz Fibonacci Notes 6. A Generating Function
for Halsey's Fibonacci Function . . . . 276--280
Raymond E. Whitney Advanced Problems and Solutions . . . . 281--284
A. P. Hillman Elementary Problems and Solutions . . . 285--288
A. F. Horadam Generating Identities for Generalized
Fibonacci and Lucas Sequences . . . . . 289--292
Paul S. Bruckman On the Evaluation of Certain Infinite
Series by Elliptic Functions . . . . . . 293--310
H. W. Gould and
J. B. Kim and
V. E. Hoggatt, Jr. Sequences Associated with $t$-Ary Coding
of Fibonacci's Rabbits . . . . . . . . . 311--318
Thomas B. Kirkpatrick, Jr. Fibonacci Sequences and Additive
Triangles of Higher Order and Degree . . 319--322
V. E. Hoggatt, Jr. and
G. E. Bergum A Problem of Fermat and the Fibonacci
Sequence . . . . . . . . . . . . . . . . 323--330
Walter E. Beck and
Rudolph M. Najar More Reduced Amicable Pairs . . . . . . 331--332
R. A. Brualdi and
J. Csima Fibonacci Sequence and Extremal
Stochastic Matrices . . . . . . . . . . 333--335
Edward T. Frankel Bell's Imperfect Perfect Numbers . . . . 336
Walter E. Beck and
Rudolph M. Najar Fixed Points of Certain Arithmetic
Functions . . . . . . . . . . . . . . . 337--341
Anonymous Fibonacci Association Research
Conference . . . . . . . . . . . . . . . 342
I. L. Iakin Generalized Quaternions of Higher Order 343--345
Anonymous Letter to the Editor . . . . . . . . . . 346
Peter Kiss and
Bui Minh Phong On the Connection Between the Rank of
Apparition of a Prime $p$ in Fibonacci
Sequence and the Fibonacci Primitive
Roots . . . . . . . . . . . . . . . . . 347--349
A. L. Iakin Generalized Quaternions with Quaternion
Components . . . . . . . . . . . . . . . 350--352
M. J. DeLeon Fibonacci Primitive Roots and the Period
of the Fibonacci Numbers Modulo $p$ . . 353--355
W. E. Greig On Sums of Fibonacci-Type Reciprocals 356--358
Stephen W. Smith and
Dean B. Priest Row and Rising Diagonal Sums for a Type
of Pascal Triangle . . . . . . . . . . . 359--360
Anonymous Addendum . . . . . . . . . . . . . . . . 361
J. W. Layman Certain General Binomial--Fibonacci Sums 362--366
V. E. Hoggatt, Jr. A Note on the Summation of Squares . . . 367--369
Brother Alfred Brousseau Fibonacci Numbers in Diatoms? . . . . . 370
Raymond E. Whitney Advanced Problems and Solutions . . . . 371--374
A. P. Hillman Elementary Problems and Solutions . . . 375--377
Anonymous Volume Index . . . . . . . . . . . . . . 378
A. G. Shannon Fibonacci and Lucas Numbers and the
Complexity of a Graph . . . . . . . . . 1--3
Hugo S. Sun Embedding a Group in the $p$ th Powers 4
Dean R. Hickerson Identities Relating the Number of
Partitions into an Even and Odd Number
of Parts. II . . . . . . . . . . . . . . 5--6
James E. Desmond On the Existence of the Rank of
Apparition of $m$ in the Lucas Sequence 7--10
L. Carlitz Recurrences of the Third Order and
Related Combinatorial Identities . . . . 11--18
J. L. Brown, Jr. Some Sequence-to-Sequence
Transformations which Preserve
Completeness . . . . . . . . . . . . . . 19--22
Dean R. Hickerson An Identity Relating Compositions and
Partitions . . . . . . . . . . . . . . . 23--26
A. G. Shannon On the Multiplication of Recursive
Sequences . . . . . . . . . . . . . . . 27--32
A. F. Horadam Diagonal Functions . . . . . . . . . . . 33--36
Douglas Hensley Fibonacci Tiling and Hyperbolas . . . . 37--40
J. L. Brown, Jr. and
V. E. Hoggatt, Jr. A Primer for the Fibonacci Numbers, Part
XVI, The Central Column Sequence . . . . 41--46
Joseph J. Heed and
Lucille Kelly Entry Points of the Fibonacci Sequence
and the Euler $ \phi $ Function . . . . 47--50
W. G. Brady More on Benford's Law . . . . . . . . . 51--52
Brother Alfred Brousseau Formula Development Through Finite
Differences . . . . . . . . . . . . . . 53--66
Marjorie Bicknell-Johnson A Golden Double Crostic . . . . . . . . 67--69
M. D. Hendy Stolarsky's Distribution of the Positive
Integers . . . . . . . . . . . . . . . . 70--80
J. C. Butcher On a Conjecture Concerning a Set of
Sequences Satisfying the Fibonacci
Difference Equation . . . . . . . . . . 81--83
Richard Austin and
Richard Guy Binary Sequences without Isolated Ones 84--85
James E. Desmond On the Equality of Periods of Different
Moduli in the Fibonacci Sequence . . . . 86--87
A. P. Hillman Elementary Problems and Solutions . . . 88--91
Raymond E. Whitney Advanced Problems and Solutions . . . . 92--96
M. W. Bunder More Fibonacci Functions . . . . . . . . 97--98
A. G. Shannon Pellian Diophantine Sequences . . . . . 99--102
L. Toscano Some Results for Generalized Bernoulli,
Euler, Stirling Numbers . . . . . . . . 103--111
Pamilla Graves Smith Expansion . . . . . . . . . . . . . . . 112
G. E. Bergum and
V. E. Hoggatt, Jr. A Combinatorial Problem Involving
Recursive Sequences and Tridiagonal
Matrices . . . . . . . . . . . . . . . . 113--117
Peter G. Anderson On the Formula $ \pi = 2 \sum \arccot
f_{2k + 1} $ . . . . . . . . . . . . . . 118
M. B. Gregory and
J. M. Metzger Fibonacci Sine Sequences . . . . . . . . 119--120
Rodney T. Hansen General Identities for Linear Fibonacci
and Lucas Summations . . . . . . . . . . 121--127
David Zeitlin An Inequality for a Class of Polynomials 128
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson A Primer for the Fibonacci Numbers XVII:
Generalized Fibonacci Numbers Satisfying
$ u_{n + 1} u_{n - 1} - u_n^2 = \pm 1 $ 128--137
L. Carlitz and
V. E. Hoggatt, Jr. Generalized Eulerian Numbers and
Polynomials . . . . . . . . . . . . . . 138--146
A. F. Horadam Wythoff Pairs . . . . . . . . . . . . . 147--151
Raymond E. Whitney Geometric Sequences and the Initial
Digit Problem . . . . . . . . . . . . . 152--153
Anonymous Addenda to Advanced Problems and
Solutions . . . . . . . . . . . . . . . 154
Burton W. Jones A Second Variation on a Problem of
Diophantus and Davenport . . . . . . . . 155--165
W. E. Greig On Generalized $ G_{j, k} $ Numbers . . 166--170
F. A. Zenz The Fluid Mechanics of Bubbling Beds . . 171--183
A. P. Hillman Elementary Problems and Solutions . . . 184--187
Raymond E. Whitney Advanced Problems and Solutions . . . . 188--192
Robert E. Dressler and
Louis Pigno Interpolation of Fourier Transforms on
Sums of Fibonacci Numbers . . . . . . . 193--194
Robert E. Dressler and
Louis Pigno Topological, Measure Theoretic and
Analytic Properties of the Fibonacci
Numbers . . . . . . . . . . . . . . . . 195--197
Donald E. Knuth and
Michael S. Paterson Identities from Partition Involutions 198--212
A. S. Gladwin Expansion of the Fibonacci Number $ F_{n
m} $ in $n$ th Powers of Fibonacci or
Lucas Numbers . . . . . . . . . . . . . 213--215
Leonard Carlitz Some Polynomials Related to Fibonacci
and Eulerian Numbers . . . . . . . . . . 216--226
Leonard Carlitz A Recurrence Suggested by a
Combinatorial Problem . . . . . . . . . 227--242
Leonard Carlitz Some Remarks on a Combinatorial Identity 243--248
Leonard Carlitz Enumeration of Certain Weighted
Sequences . . . . . . . . . . . . . . . 249--254
Leonard Carlitz The Number of Derangements of a Sequence
with Given Specification . . . . . . . . 255--258
Leonard Carlitz Enumeration of Permutations by Sequences 259--268
Walter Gerdes Generalized Tribonacci Numbers and Their
Convergent Sequences . . . . . . . . . . 269--275
Paul Cull and
Jeffery De Curtins Knight's Tour Revisited . . . . . . . . 276--284
Gerald E. Bergum and
Verner E. Hoggatt, Jr. A Family of Tridiagonal Matrices . . . . 285--288
Verner E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Properties of Generating Functions of a
Convolution Array . . . . . . . . . . . 289--295
O. D. Anderson Some More Pattern from Pascal's Triangle 296--301
Marion Beiter Coefficients of the Cyclotomic
Polynomial $ F_{3qr}(x) $ . . . . . . . 302--306
J. L. Brown, Jr. Simplified Proof of a Greatest Integer
Function Theorem . . . . . . . . . . . . 307--309
A. Eswarathasan On Square Pseudo-Fibonacci Numbers . . . 310--314
Joseph De Vita Fibonacci, Insects, and Flowers . . . . 315--317
Rosalind Guaraldo On the Density of the Image Sets of
Certain Arithmetic Functions --- I . . . 318--326
E. E. Guerin Matrices and Convolutions of Arithmetic
Functions . . . . . . . . . . . . . . . 327--334
James M. Suttenfield, Jr. A New Series . . . . . . . . . . . . . . 335--343
Marcellus E. Waddill Some Properties of a Generalized
Fibonacci Sequence Modulo $m$ . . . . . 344--353
Leon Bernstein An Invariant for Combinatorial
Identities . . . . . . . . . . . . . . . 354--369
E. M. Horadam Solved, Semi-Solved, and Unsolved
Problems in Generalized Integers: a
Survey . . . . . . . . . . . . . . . . . 370--380
S. P. Mohanty The Number of Primes is Infinite . . . . 381--384
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Convolution Arrays for Jacobsthal and
Fibonacci Polynomials . . . . . . . . . 385--402
Andrew Vince The Fibonacci Sequence Modulo $N$ . . . 403--406
J. A. H. Hunter Congruent Primes of Form $ (8 r + 1) $ 407--410
Leonard Carlitz Some Classes of Fibonacci Sums . . . . . 411--425
Marjorie Bicknell-Johnson Fibonacci Chromotology or How to Paint
Your Rabbit . . . . . . . . . . . . . . 426--427
Rosalind Guaraldo On the Density of the Image Sets of
Certain Arithmetic Functions --- II . . 428--434
Helaman Rolfe Pratt Ferguson The Fibonacci Pseudogroup,
Characteristic Polynomials and
Eigenvalues of Tridiagonal Matrices,
Periodic Linear Recurrence Systems and
Application to Quantum Mechanics . . . . 435--446
Leonard E. Fuller Vectors Whose Elements Belong to a
Generalized Fibonacci Sequence . . . . . 447--450
Ray Steiner On $N$ th Powers in the Lucas and
Fibonacci Series . . . . . . . . . . . . 451--458
Jim Flanigan Generalized Two-Pile Fibonacci Nim . . . 459--469
Ray Steiner On $k$ th-Power Numerical Centers . . . 470--471
V. E. Hoggatt, Jr. and
A. P. Hillman A Property of Wythoff Pairs . . . . . . 472
A. P. Hillman Elementary Problems and Solutions . . . 473--476
Raymond E. Whitney Advanced Problems and Solutions . . . . 477--480
Rosalind Guaraldo On the Density of the Image Sets of
Certain Arithmetic Functions --- III . . 481--487
H. W. Gould Evaluation of Sum of Convolved Powers
Using Stirling and Eulerian Numbers . . 488--496
Heiko Harborth $b$-Adic Numbers in Pascal's Triangle
Modulo $b$ . . . . . . . . . . . . . . . 497--500
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Divisibility Properties of Polynomials
in Pascal's Triangle . . . . . . . . . . 501--512
Paul Larson The Golden Section in the Earliest
Notated Western Music . . . . . . . . . 513--514
Neville Robbins On Fibonacci Numbers Which are Powers 515--517
B. de La Rosa Primes, Powers, and Partitions . . . . . 518--522
G. L. Cohen On Odd Perfect Numbers . . . . . . . . . 523--526
Irving Adler A Simple Continued Fraction Represents a
Mediant Nest of Intervals . . . . . . . 527--529
W. E. Greig Folded Sequences and Bode's Problem . . 530--538
Mark Finkelstein and
Robert Whitley Fibonacci Numbers in Coin Tossing
Sequences . . . . . . . . . . . . . . . 539--540
Clark Kimberling Strong Divisibility Sequences with
Nonzero Initial Term . . . . . . . . . . 541--543
W. Herget Minimum Periods Modulo $n$ for Bernoulli
Numbers . . . . . . . . . . . . . . . . 544--547
Hansraj Gupta The Rank-Vector of a Partition . . . . . 548--551
Hansraj Gupta The Andrews Formula for Fibonacci
Numbers . . . . . . . . . . . . . . . . 552--554
H. W. Gould Operational Formulas for Unusual
Fibonacci Series . . . . . . . . . . . . 555--560
Harvey J. Hindin A Figurate Number Curiosity: Every
Integer is a Quadratic Function of a
Figurate Number . . . . . . . . . . . . 561
A. P. Hillman Elementary Problems and Solutions . . . 562--565
Raymond E. Whitney Advanced Problems and Solutions . . . . 566--569
Anonymous Volume Index . . . . . . . . . . . . . . 570
Marjorie Bicknell-Johnson Pythagorean Triples Containing Fibonacci
Numbers: Solution for $ F_n^2 \pm F_k^2
= K^2 $ . . . . . . . . . . . . . . . . 1--12
Clark Kimberling Strong Divisibility Sequences and Some
Conjectures . . . . . . . . . . . . . . 13--17
Clark Kimberling Greatest Common Divisors of Sums and
Differences of Fibonacci, Lucas and
Chebyshev Polynomials . . . . . . . . . 18--22
Stephen John Turner Probability via the $N$ th Order
Fibonacci-$T$ Sequence . . . . . . . . . 23--28
Charles R. Wall Some Congruences Involving Generalized
Fibonacci Numbers . . . . . . . . . . . 29--33
F. W. Light, Jr. Enumeration of Truncated Latin
Rectangles . . . . . . . . . . . . . . . 34--36
John Boardman The Normal Modes of a Hanging Oscillator
of Order $N$ . . . . . . . . . . . . . . 37--39
Norvald Midttun Congruences for Certain Fibonacci
Numbers . . . . . . . . . . . . . . . . 40--41
Paul S. Bruckman Some Divisibility Properties of
Generalized Fibonacci Sequences . . . . 42--48
William J. O'Donnell A Note on a Pell-Type Sequence . . . . . 49--50
A. Allard and
P. Lecomte Periods and Entry Points in Fibonacci
Sequence . . . . . . . . . . . . . . . . 51--57
Claudia Smith and
Verner E. Hoggatt, Jr. Generating Functions of Central Values
in Generalized Pascal Triangles . . . . 58--66
James C. Owings, Jr. Solution of $ \binom (y + 1, x) = \binom
(y, x + 1) $ in Terms of Fibonacci
Numbers . . . . . . . . . . . . . . . . 67--68
David A. Anderson and
Milton W. Loyer The Diophantine Equation $ N b^2 = c^2 +
N + 1 $ . . . . . . . . . . . . . . . . 69--70
Joseph Ercolano Matrix Generators of Pell Sequences . . 71--76
William J. O'Donnell Two Theorems Concerning Hexagonal
Numbers . . . . . . . . . . . . . . . . 77--79
B. H. Neumann and
L. G. Wilson Some Sequences like Fibonacci's . . . . 80--83
V. E. Hoggatt, Jr. and
A. P. Hillman Nearly Linear Functions . . . . . . . . 84--89
A. P. Hillman Elementary Problems and Solutions . . . 90--93
Raymond E. Whitney Advanced Problems and Solutions . . . . 94--96
James E. Joseph Maximum Cardinalities for Topologies on
Finite Sets . . . . . . . . . . . . . . 97--102
Christine Giuli and
Robert Giuli A Primer on Stern's Diatomic Sequence 103--107
Louis Comtet A Multinomial Generalization of a
Binomial Identity . . . . . . . . . . . 108--110
Lawrence Somer Which Second-Order Linear Integral
Recurrences Have Almost All Primes as
Divisors? . . . . . . . . . . . . . . . 111--115
William I. McLaughlin Note on a Tetranacci Alternative to
Bode's Law . . . . . . . . . . . . . . . 116--117
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Reflections Across Two and Three Glass
Plates . . . . . . . . . . . . . . . . . 118--141
A. Eswarathasan On Pseudo-Fibonacci Numbers of the Form
$ 2 S^2 $, Where $S$ is an Integer . . . 142--146
Gerald E. Bergum and
Verner E. Hoggatt, Jr. Infinite Series with Fibonacci and Lucas
Polynomials . . . . . . . . . . . . . . 147--150
Edward M. Reingold A Note on $3$-$2$ Trees . . . . . . . . 151--157
J. C. Ahuja and
E. A. Enneking Concavity Property and a Recurrence
Relation for Associated Lah Numbers . . 158--161
J. C. de Almeida Azevedo Fibonacci Numbers . . . . . . . . . . . 162--164
Norman Woo A Note on Basic $M$-Tuples . . . . . . . 165--167
David W. Ballew and
Ronald C. Weger Pythagorean Triples and Triangular
Numbers . . . . . . . . . . . . . . . . 168--171
Haig E. Bohigian Extensions of the W. Mnich Problem . . . 172--177
Harvey Cohn Growth Types of Fibonacci and Markoff 178--183
A. P. Hillman Elementary Problems and Solutions . . . 184--187
Anonymous Errata . . . . . . . . . . . . . . . . . 188
Raymond E. Whitney Advanced Problems and Solutions . . . . 189--192
Rada Higgins More in the Theory of Sequences . . . . 193--197
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson and
Richard Sarsfield A Generalization of Wythoff's Game . . . 198--211
A. S. Adikesavan and
S. Narayanaswami A Modification of Goka's Binary Sequence 212--219
Leonard Carlitz Restricted Multipartite Compositions . . 220--227
F. P. Sayer The Recurrence Relation $ (r + 1)f_{r +
1} = x f_r^\prime + (K - r + 1) x^2 f_{r
- 1} $ . . . . . . . . . . . . . . . . . 228--238
Jean-Pierre Gallinar Fibonacci Ratio in a Thermodynamical
Case . . . . . . . . . . . . . . . . . . 239--240
H. S. Sun On Groups Generated by the Squares . . . 241--245
Christine Giuli and
Robert Giuli A Primer on Stern's Diatomic Sequence
--- II . . . . . . . . . . . . . . . . . 246--247
A. F. Horadam Sums of Products: An Extension . . . . . 248--249
Murray Hochberg A Conjecture in Game Theory . . . . . . 250--252
Louis W. Shapiro The Cycle of Six . . . . . . . . . . . . 253--258
Arnold L. Rosenberg Profile Numbers . . . . . . . . . . . . 259--263
Claudia Smith and
Verner E. Hoggatt, Jr. A Study of the Maximal Values in
Pascal's Quadrinomial Triangle . . . . . 264--268
Peter Heichelheim The Study of Positive Integers $ (a, b)
$ Such that $ a b + 1 $ is a Square . . 269--274
Frederick Stern Absorption Sequences . . . . . . . . . . 275--280
A. P. Hillman Elementary Problems and Solutions . . . 281--285
Raymond E. Whitney Advanced Problems and Solutions . . . . 286--288
Gerald Weinstein An Algorithm for Packing Complements of
Finite Sets of Integers . . . . . . . . 289--292
Marjorie Bicknell-Johnson Addenda to ``Pythagorean Triples
Containing Fibonacci Numbers: Solutions
for $ F_n^2 \pm F_k^2 = K^2 $'' . . . . 293
A. G. Shannon and
A. F. Horadam Special Recurrence Relations Associated
with the Sequence $ \{ w_n(a, b; p, q)
\} $ . . . . . . . . . . . . . . . . . . 294--298
M. E. Cohen and
H. Sun On Some Extensions of the Wang--Carlitz
Identity . . . . . . . . . . . . . . . . 299--305
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Representations of Integers in Terms of
Greatest Integer Functions and the
Golden Section Ratio . . . . . . . . . . 306--317
Christine Giuli and
Robert Giuli A Primer on Stern's Diatomic Sequence:
Part III: Additional Results . . . . . . 318--320
Leonard Carlitz Restricted Compositions II . . . . . . . 321--327
A. F. Horadam Chebyshev and Fermat Polynomials for
Diagonal Functions . . . . . . . . . . . 328--332
Joseph Arkin and
V. E. Hoggatt, Jr. and
E. G. Strasus On Euler's Solution of a Problem of
Diophantus . . . . . . . . . . . . . . . 333--339
T. Antony Davis and
Rudolf Altevogt Golden Mean of the Human Body . . . . . 340--343
A. G. Shannon A Recurrence Relation for Generalized
Multinomial Coefficients . . . . . . . . 344--346
A. G. Shannon Generalized Fibonacci Numbers as
Elements of Ideals . . . . . . . . . . . 347--348
A. G. Shannon A Generalization of Hilton's Partition
of Horadam's Sequences . . . . . . . . . 349--357
Graham Lord and
Herve G. Morin Degeneracy of Transformed Complete
Sequences . . . . . . . . . . . . . . . 358--360
Susumu Morito and
Harvey M. Salkin Finding the General Solution of a Linear
Diophantine Equation . . . . . . . . . . 361--368
A. P. Hillman Elementary Problems and Solutions . . . 369--373
Raymond E. Whitney Advanced Problems and Solutions . . . . 374--378
Anonymous Index of Advanced Problems . . . . . . . 379
Anonymous Volume Index . . . . . . . . . . . . . . 380
John A. Ewell Recurrences for Two Restricted Partition
Function . . . . . . . . . . . . . . . . 1--2
A. F. Horadam Extensions of a Paper on Diagonal
Functions . . . . . . . . . . . . . . . 3--8
J. S. Frame Factors of the Binomial Circulant
Determinant . . . . . . . . . . . . . . 9--23
Ronald C. Read A Note on Tiling Rectangles with
Dominoes . . . . . . . . . . . . . . . . 24--27
Gerald E. Bergum and
Verner E. Hoggatt, Jr. Some Extensions of Wythoff Pair
Sequences . . . . . . . . . . . . . . . 28--32
F. R. Baudert The Apollonius Problem . . . . . . . . . 33
L. A. G. Dresel Letter to the Editor . . . . . . . . . . 34
W. G. Waller and
Mahadev Banerjee Summation of the Series $ y^n + (y +
1)^n + \cdots {} + x^n $ . . . . . . . . 35
Claudia Smith and
Verner E. Hoggatt, Jr. Roots of $ (H - L) / 15 $ Recurrence
Equations in Generalized Pascal
Triangles . . . . . . . . . . . . . . . 36--42
A. G. T. Babu and
Wei Shen Hsia A Note on the Multiplication of Two $ 3
\times 3 $ Fibonacci-Rowed Matrices . . 43
T. E. Stanley Powers of the Period Function for the
Sequence of Fibonacci Numbers . . . . . 44
T. E. Stanley Some Remarks on the Periodicity of the
Sequence of Fibonacci Numbers --- II . . 45--46
Steven Kahan Mutually Counting Sequences . . . . . . 47--50
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Multisection of the Fibonacci
Convolution Array and Generalized Lucas
Squence . . . . . . . . . . . . . . . . 51--57
Leonard Carlitz Some Restricted Multiple Sums . . . . . 58--65
Leonard Carlitz Some Remarks on the Bell Numbers . . . . 66--72
A. G. Shannon Some Lacunary Recurrence Relations . . . 73--79
Verner E. Hoggatt, Jr. and
Hugh Edgar Another Proof that $ \phi (F_n) \equiv 0
\bmod 4 $ for All $ n > 4 $ . . . . . . . 80--81
David L. Russell Letter to the Editor . . . . . . . . . . 82
Anonymous Corrections . . . . . . . . . . . . . . 82--83
A. P. Hillman Elementary Problems and Solutions . . . 84--89
Raymond E. Whitney Advanced Problems and Solutions . . . . 90--96
V. E. Hoggatt, Jr. and
A. P. Hillman Recursive, Spectral, and Self-Generating
Sequences . . . . . . . . . . . . . . . 97--103
Gary L. Mullen Local Permutation Polynomials Over $ Z_p
$ . . . . . . . . . . . . . . . . . . . 104--107
Clark Kimberling Generalized Cyclotomic Polynomials,
Fibonacci Cyclotomic Polynomials, and
Lucas Cyclotomic Polynomials . . . . . . 108--125
Leonard E. Fuller Geometric Recurrence Relation . . . . . 126--128
Leonard E. Fuller Representations for $ r, s $ Recurrence
Relations . . . . . . . . . . . . . . . 129--134
Sahib Singh Thoro's Conjecture and Allied
Divisibility Property of Lucas Numbers 135--136
Neville Robbins A Class of Solutions of the Equation $
\sigma (n) = 2 n + t $ . . . . . . . . . 137--146
L. Carlitz Weighted Stirling Numbers of the First
and Second Kind --- I . . . . . . . . . 147--162
O. R. Ainsworth and
Joseph E. Morris, Jr. A Property of Quasi-Orthogonal
Polynomials . . . . . . . . . . . . . . 163--164
Andrzej Wi\keckowski On Some Systems of Diophantine equations
Including the Algebraic Sum of
Triangular Numbers . . . . . . . . . . . 165--169
Joseph Arkin and
V. E. Hoggatt, Jr. and
E. G. Straus On Euler's Solution to a Problem of
Diophantus --- II . . . . . . . . . . . 170--176
L. Carlitz Fibonacci Notes 6. Zero-One Sequence
Once More . . . . . . . . . . . . . . . 177--184
Anonymous Book Announcement . . . . . . . . . . . 185
A. P. Hillman Elementary Problems and Solutions . . . 186--189
Raymond E. Whitney Advanced Problems and Solutions . . . . 190--192
Clark Kimberling Generating Functions of Linear
Divisibility Sequences . . . . . . . . . 193--207
Gary L. Mullen Local Permutation Polynomials in Three
Variables over $ Z_p $ . . . . . . . . . 208--213
Mordechai Lewin Some Combinatorial Identities . . . . . 214--219
V. E. Hoggatt, Jr. Additive Partitions of the Positive
Integers . . . . . . . . . . . . . . . . 220--225
G. Kreweras The Number of More or Less ``Regular''
Permutations . . . . . . . . . . . . . . 226--228
Aaron B. Budgor Star Polygons, Pascal's Triangle, and
Fibonacci Numbers . . . . . . . . . . . 229--230
Masaji Yamada A Convergence Proof about an Integral
Sequence . . . . . . . . . . . . . . . . 231--241
L. Carlitz Weighted Stirling Numbers of the First
and Second Kind --- II . . . . . . . . . 242--257
Harvey J. Hindin A Theorem Concerning Heptagonal Numbers 258
Harvey J. Hindin An Alternate Representation for Césaro's
Fibonacci--Lucas Identity . . . . . . . 259--260
Jack M. Pollin and
I. J. Schoenberg On the Matrix Approach to Fibonacci
Numbers and the Fibonacci Pseudoprimes 261--267
G. Walther Free Group and Fibonacci Sequence . . . 268--272
A. P. Hillman Elementary Problems and Solutions . . . 273--279
Raymond E. Whitney Advanced Problems and Solutions . . . . 280--288
Marjorie Bicknell-Johnson In Memoriam --- Verner E. Hoggatt, Jr. 289
Anne Silva and
Verner E. Hoggatt, Jr. Generalized Fibonacci Number . . . . . . 290--299
Robert J. Epp and
Thomas S. Ferguson A Note on Take-Away Games . . . . . . . 300--302
F. T. Howard Associated Stirling Numbers . . . . . . 303--315
Lawrence Somer The Divisibility Properties of Primary
Lucas Recurrences with Respect to Primes 316--333
Clark Kimberling Mixing Properties of Mixed Chebyshev
Polynomials . . . . . . . . . . . . . . 334--340
Michael Creutz and
R. M. Sternheimer On the Convergence of Iterated
Exponentiation --- I . . . . . . . . . . 341--346
L. Carlitz The Number of Permutations with a Given
Number of Sequences . . . . . . . . . . 347--352
Clark Kimberling Four Composition Identities for
Chebyshev Polynomials . . . . . . . . . 353--369
A. P. Hillman Elementary Problems and Solutions . . . 370--374
Raymond E. Whitney Advanced Problems and Solutions . . . . 375--381
Anonymous Volume Index . . . . . . . . . . . . . . 382
John Gill and
Gary Miller Newton's Method and Ratios of Fibonacci
Numbers . . . . . . . . . . . . . . . . 1--3
M. J. DeLeon A Characterization of the Fundamental
Solutions to Pell's Equation $ u^2 - D
v^2 = C $ . . . . . . . . . . . . . . . 4--5
Daniel Minoli Structural Issues for Hyperperfect
Numbers . . . . . . . . . . . . . . . . 6--13
Robert P. Backstrom On Reciprocal Series Related to
Fibonacci Numbers with Subscripts in
Arithmetic Progression . . . . . . . . . 14--20
Masao Kishore On the Equation $ \sigma (m) \sigma (n)
= (m + n)^2 $ . . . . . . . . . . . . . 21--23
Leonard E. Fuller A Special $m$ th-Order Recurrence
Relation . . . . . . . . . . . . . . . . 24--27
D. W. Bange and
A. E. Barkauskas and
P. J. Slater Fibonacci Numbers in Tree Counts for
Maximal Outerplane and Related Graphs 28--34
Duane W. DeTemple A New Angle on the Geometry of the
Fibonacci Numbers . . . . . . . . . . . 35--38
J. C. Lagarias and
D. P. Weisser Fibonacci and Lucas Cubes . . . . . . . 39--42
Michael J. Magazine The Number of States in a Class of
Serial Queueing Systems . . . . . . . . 43--44
G. D. Prichett and
A. L. Ludington and
J. F. Lapenta The Determination of All Decadic
Kaprekar Constants . . . . . . . . . . . 45--52
C. T. Long The Decimal Expansion of $ 1 / 89 $ and
Related Results . . . . . . . . . . . . 53--55
Furio Alberti A Root Property of a Psi-Type Equation 56
Dennis C. Smolarski and
Leonard F. Klosinski Recognition Algorithms for Fibonacci
Numbers . . . . . . . . . . . . . . . . 57--60
Robert S. Garfinkel and
Stanley M. Selkow On Some Conjectures of Gould on the
Parities of the Binomial Coefficients 61--63
Leonard E. Fuller Solutions for General Recurrence
Relations . . . . . . . . . . . . . . . 64--68
M. E. Cohen and
H. S. Sun On Generating Functions and Double
Series Expansions . . . . . . . . . . . 69--73
James V. Peters An Equivalent Form of Benford's Law . . 74--75
J. Arkin and
K. Singh A New Type Magic Latin $3$-Cube of Order
Ten . . . . . . . . . . . . . . . . . . 76--81
C. J. Harman Complex Fibonacci Numbers . . . . . . . 82--86
A. P. Hillman Elementary Problems and Solutions . . . 87--92
Raymond E. Whitney Advanced Problems and Solutions . . . . 93--96
Brian Alspach and
Katherine Heinrich Perfect Magic Cubes of Order $ 4^m $ . . 97--105
Leonard E. Fuller Generating Functions for Recurrence
Relations . . . . . . . . . . . . . . . 106--109
Lawrence Somer The Residues of $ n^n $ Modulo $p$ . . . 110--116
Mary E. Gbur A Generalization of a Problem of
Stolarsky . . . . . . . . . . . . . . . 117--120
J. Knopfmacher Initial Digits in Number Theory . . . . 121--126
Robert Chen and
Alan Zame Fibonacci Numbers and Stopping Times . . 127--130
Robert R. Hill and
Kenneth L. Goldstein A Non-Fibonacci Search Plan with
Fibonacci-Like Results . . . . . . . . . 131--136
Ira Gessel Congruences for Bell and Tangent Numbers 137--143
Julio R. Bastida and
M. J. DeLeon A Quadratic Property of Certain Linearly
Recurrent Sequences . . . . . . . . . . 144--146
Julio R. Bastida The Determination of Certain Fields of
Invariants . . . . . . . . . . . . . . . 147--148
Constantine Kliorys Fibonacci Number Identities from
Algebraic Units . . . . . . . . . . . . 149--152
B. Gleijeses Points at Mutual Integral Distances in $
S^n $ . . . . . . . . . . . . . . . . . 153--159
Robert Schoen Means, Circles, Right Triangles, and the
Fibonacci Ratio . . . . . . . . . . . . 160--162
Calvin T. Long A Limited Arithmetic on Simple Continued
Fractions --- III . . . . . . . . . . . 163--174
Lawrence C. Washington Benford's Law for Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 175--177
Rasul A. Khan A Simple Derivation of a Formula for $
\sum_{k = 1}^n k^r $ . . . . . . . . . . 177--179
Shiro Ando A Note on the Polygonal Numbers . . . . 180--183
A. P. Hillman Elementary Problems and Solutions . . . 184--188
Raymond E. Whitney Advanced Problems and Solutions . . . . 189--192
Howard Eves Hail to Thee, Blithe Spirit! . . . . . . 193--195
Marjorie Bicknell-Johnson Diagonal Sums in the Harmonic Triangle 196--199
L. Carlitz Some Generalizations of a Binomial
Identity Conjectured by Hoggatt . . . . 200--207
Paul Erd\Hos Some Extremal Problems on Divisibility
Properties of Sequences of Integers . . 208--213
Lester H. Lange Hommage \`a Archim\`ede . . . . . . . . 214--218
David A. Klarner The Ubiquitous Rational Sequence . . . . 219--227
Krishnaswami Alladi On the Probability That $n$ and $ \Omega
(n) $ are Relatively Prime . . . . . . . 228--232
A. P. Hillman Proportional Allocation in Integers . . 233--239
A. F. Horadam and
A. G. Shannon Irrational Sequence-Generated Factors of
Integers . . . . . . . . . . . . . . . . 240--249
H. W. Gould A History of the Fibonacci $ {Q}
$-Matrix and a Higher-Dimensional
Problem . . . . . . . . . . . . . . . . 250--256
Calvin T. Long Some Divisibility Properties of Pascal's
Triangle . . . . . . . . . . . . . . . . 257--263
Karel De Bouv\`ere Fibonacci Induced Groups and Their
Hierarchies . . . . . . . . . . . . . . 264--270
Dmitri Thoro and
Hugh Edgar Exploring an Algorithm . . . . . . . . . 271--275
Dave Logothetti An Implicit Triangle of Numbers . . . . 276--279
Clark Kimberling Fractional Parts $ (n r - s) $, Almost
Arithmetic Sequences, and Fibonacci
Numbers . . . . . . . . . . . . . . . . 280--284
Ray Steiner On the ``$ Q X + 1 $ Problem,'' $Q$ Odd 285--288
Joseph Arkin and
E. G. Straus Orthogonal Latin Systems . . . . . . . . 289--292
Ray Steiner On the ``$ Q X + 1 $ Problem,'' $Q$ Odd
--- II . . . . . . . . . . . . . . . . . 293--296
Bart F. Rice and
Robert Ward Binary Words with Minimal
Autocorrelation at Offset One . . . . . 297--312
William Squire Fibonacci Cubature . . . . . . . . . . . 313
S. P. Mohanty On a Problem of S. J. Bezuszka and M. J.
Kenney on Cyclic Difference of Pairs of
Integers . . . . . . . . . . . . . . . . 314--317
John R. Burke and
William A. Webb Asymptotic Behavior of Linear
Recurrences . . . . . . . . . . . . . . 318--321
A. L. Iakin Anomalies in Higher-Order Conjugate
Quaternions: a Clarification . . . . . . 322--325
Michael Creutz and
R. M. Sternheimer On the Convergence of Iterated
Exponentiation --- II . . . . . . . . . 326--335
David L. Russell Summation of Second-Order Recurrence
Terms and Their Squares . . . . . . . . 336--339
Samuel S. Wagstaff, Jr. Iterating the Product of Shifted Digits 340--346
Refael Hassin On Maximizing Functions by Fibonacci
Search . . . . . . . . . . . . . . . . . 347--350
Donald J. Mintz $ 2, 3 $ Sequence as Binary Mixture . . 351--360
Robert D. Girse Identities for Certain Partition
Functions and Their Differences . . . . 361--368
Neville Robbins Fibonacci and Lucas Numbers of the Forms
$ w^2 - 1, w^3 \pm 1 $ . . . . . . . . . 369--372
Michael D. Hirschhorn The Andrews Formula for Fibonacci
Numbers . . . . . . . . . . . . . . . . 373--374
J. H. Clarke and
A. G. Shannon Some Constraints on Fermat's Last
Theorem . . . . . . . . . . . . . . . . 375--376
A. P. Hillman Elementary Problems and Solutions . . . 377--380
Raymond E. Whitney Advanced Problems and Solutions . . . . 381--384
Gregory Wulczyn A Generalized Extension of Some
Fibonacci--Lucas Identities to Primitive
Unit Identities . . . . . . . . . . . . 385--390
Carl P. McCarty A Formula for Tribonacci Numbers . . . . 391--392
A. F. Horadam and
S. Pethe Polynomials Associated with Gegenbauer
Polynomials . . . . . . . . . . . . . . 393--397
L. Carlitz Enumeration of Permutations by Sequences
--- II . . . . . . . . . . . . . . . . . 398--405
Roger Fischler How to Find the ``Golden Number''
without Really Trying . . . . . . . . . 406--409
A. L. Iakin Extended Binet Forms for Generalized
Quaternions of Higher Order . . . . . . 410--413
Richard H. Hudson and
C. F. Winans A Complete Characterization of the
Decimal Fractions That Can be
Represented as $ \sum 10^{-k (i + 1)}
{F}_{ai} $, Where $ F_{ai} $ is the $ a
i $ th Fibonacci Number . . . . . . . . 414--421
M. E. Cohen and
H. S. Sun On Some Extensions of the
Meixner--Weisner Generating Functions 422--425
Clark Kimberling Almost Arithmetic Sequences and
Complementary Systems . . . . . . . . . 426--432
Andrew M. Rockett Sums of the Inverses of Binomial
Coefficients . . . . . . . . . . . . . . 433--436
Hans Herda Tiling the Plane with Incongruent
Regular Polygons . . . . . . . . . . . . 437--439
M. W. Bunder A New Definition of Division in Rings of
Quotients of Euclidean Rings . . . . . . 440--446
Amin A. Muwafi A Recursion-Type Formula for Some
Partitions . . . . . . . . . . . . . . . 447--448
Delano P. Wegener Primitive Pythagorean Triples and the
Infinitude of Primes . . . . . . . . . . 449
Delano P. Wegener An Application of Pell's Equation . . . 450
Ch. A. Charalambides Central Factorial Numbers and Related
Expansions . . . . . . . . . . . . . . . 451--455
G. Geldenhuys On the Fibonacci Numbers Minus One . . . 456--457
Calvin T. Long Pascal's Triangle Modulo $p$ . . . . . . 458--462
Helmut Prodinger On the Number of Fibonacci Partitions of
a Set . . . . . . . . . . . . . . . . . 463--465
A. P. Hillman Elementary Problems and Solutions . . . 466--469
Raymond E. Whitney Advanced Problems and Solutions . . . . 470--476
Anonymous Volume Index . . . . . . . . . . . . . . 477
L. C. Botten On the Use of Fibonacci Recurrence
Relations in the Design of Long
Wavelength Filters and Interferometers 1--6
Michael Creutz and
R. M. Sternheimer On the Convergence of Iterated
Exponentiation --- III . . . . . . . . . 7--11
Steve Ligh and
Pat Jones Generalized Fermat and Mersenne Numbers 12--15
Helmut Prodinger and
Robert F. Tichy Fibonacci Numbers of Graphs . . . . . . 16--20
Neville Robbins Some Identities and Divisibility
Properties of Linear Second-Order
Recursion Sequences . . . . . . . . . . 21--23
L. C. Eggan and
Peter C. Eggan and
J. L. Selfridge Polygonal Products of Polygonal Numbers
and the Pell Equation . . . . . . . . . 24--27
A. N. Philippou and
A. A. Muwafi Waiting for the $K$ th Consecutive
Success and the Fibonacci Sequence of
Order $K$ . . . . . . . . . . . . . . . 28--32
William A. Webb The Length of the Four-Number Game . . . 33--35
Robert Guy Sums of Consecutive Integers . . . . . . 36--37
A. G. Shannon and
A. F. Horadam Concerning a Paper by L. G. Wilson . . . 38--40
K. Joseph Davis A Generalization of the Dirichlet
Product . . . . . . . . . . . . . . . . 41--43
A. F. Horadam and
A. G. Shannon Combinatorial Aspects of an Infinite
Pattern of Integers . . . . . . . . . . 44--50
Jim Flanigan One-Pile Time and Size Dependent
Take-Away Games . . . . . . . . . . . . 51--58
P. V. Satyanarayana Murthy Fibonacci--Cayley Numbers . . . . . . . 59--64
P. V. Satyanarayana Murthy Generalizations of Some Problems on
Fibonacci Numbers . . . . . . . . . . . 65
Mark E. Kidwell and
Clifford M. Hurvich A Variant of the Fibonacci Polynomials
Which Arises in the Gambler's Ruin
Problem . . . . . . . . . . . . . . . . 66--72
Dan Kalman Generalized Fibonacci Numbers by Matrix
Methods . . . . . . . . . . . . . . . . 73--76
J. O. Shallit Explicit Descriptions of Some Continued
Fractions . . . . . . . . . . . . . . . 77--80
Graeme L. Cohen The Nonexistence of Quasiperfect Numbers
of Certain Forms . . . . . . . . . . . . 81--84
Wayne L. McDaniel Representations of Every Integer as the
Difference of Powerful Numbers . . . . . 85--87
Anonymous Acknowledgments . . . . . . . . . . . . 88
A. P. Hillman Elementary Problems and Solutions . . . 89--92
Raymond E. Whitney Advanced Problems and Solutions . . . . 93--96
Fook-Bun Wong Ducci Processes . . . . . . . . . . . . 97--105
Wilfried Herget Minimum Periods Modulo $n$ for Bernoulli
Polynomials . . . . . . . . . . . . . . 106--110
Michael E. Mays A Note on Fibonacci Primitive Roots . . 111
L. Kuipers A Property of the Fibonacci Sequence $
(F_m), m = 0, 1, \ldots $ . . . . . . . 112--113
David L. Russell Notes on Sums of Products of Generalized
Fibonacci Numbers . . . . . . . . . . . 114--117
W. R. Spickerman Binets's Formula for the Tribonacci
Sequence . . . . . . . . . . . . . . . . 118--120
A. F. Horadam Pythagorean Triples . . . . . . . . . . 121
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Composition Arrays Generated by
Fibonacci Numbers . . . . . . . . . . . 122--128
M. J. DeLeon The Congruence $ x^n \equiv a \pmod {m}
$, Where $ (n, \phi (m)) = 1 $ . . . . . 129--134
Ch. A. Charalambides On the Enumeration of Certain
Compositions and Related Sequences of
Numbers . . . . . . . . . . . . . . . . 135--145
D. H. Fowler A Generalization of the Golden Section 146--158
Robert Schoen The Fibonacci Sequence in Successive
Partitions of a Golden Triangle . . . . 159--163
A. F. Horadam Geometry of a Generalized Simson's
Formula . . . . . . . . . . . . . . . . 164--167
Yasuichi Horibe An Entropy View of Fibonacci Trees . . . 168--178
A. P. Hillman Elementary Problems and Solutions . . . 179--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--191
Anonymous Errata . . . . . . . . . . . . . . . . . 192
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Lexicographic Ordering and Fibonacci
Representations . . . . . . . . . . . . 193--218
A. F. Horadam and
E. M. Horadam Roots of Recurrence-Generated
Polynomials . . . . . . . . . . . . . . 219--226
Leon Bernstein Primitive Pythagorean Triples . . . . . 227--241
K. C. Prasad A Note on the Farey--Fibonacci Sequence 242--244
William P. Risk Thevenin Equivalents of Ladder Networks 245--247
Anonymous Announcement of Fibonacci Research
Conference . . . . . . . . . . . . . . . 248
Mauro Boscarol A Property of Binomial Coefficients . . 249--251
Joseph McHugh Characterization of a Sequence . . . . . 252--255
John A. Ewell Consequences of Watson's
Quintuple-Product Identity . . . . . . . 256--262
John Rabung and
Jim Hyland Analysis of a Betting System . . . . . . 263--278
A. P. Hillman Elementary Problems and Solutions . . . 279--283
Raymond E. Whitney Advanced Problems and Solutions . . . . 284--288
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Sequence Transforms Related to
Representations Using Generalized
Fibonacci Numbers . . . . . . . . . . . 289--298
Richard Grassl Self-Generating Systems . . . . . . . . 299--310
Lawrence Somer Possible Periods of Primary
Fibonacci-Like Sequences with Respect to
a Fixed Odd Prime . . . . . . . . . . . 311--333
Miomir S. Stankovi\'c On a Convolution Product for the
Transform Which Maps Derivatives into
Differences . . . . . . . . . . . . . . 334--342
Elmer D. Robinson Letter to the Editor . . . . . . . . . . 343
Douglas Hensley Eulerian Numbers and the Unit Cube . . . 344--348
Shiro Ando On a System of Diophantine Equations
Concerning the Polygonal Numbers . . . . 349--353
Geröcs László Some Properties of Divisibility of
Higher-Ordered Linear Recursive
Sequences . . . . . . . . . . . . . . . 354--359
John Kerr The Existence of $K$ Orthogonal Latin
$K$-Cubes of Order $6$ . . . . . . . . . 360--362
Phyllis Lefton A Trinomial Discriminant Formula . . . . 363--365
A. P. Hillman Elementary Problems and Solutions . . . 366--371
Raymond E. Whitney Advanced Problems and Solutions . . . . 372--380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Acknowledgments . . . . . . . . . . . . 2
Neville Robbins On Fibonacci and Lucas Numbers Which are
Sums of Precisely Four Squares . . . . . 3--5
A. G. Shannon Intersections of Second-Order Linear
Recursive Sequences . . . . . . . . . . 6--12
Christopher D. Godsil and
Reinhard Razen A Property of Fibonacci and Tribonacci
Numbers . . . . . . . . . . . . . . . . 13--17
Charles R. Wall Unitary Harmonic Numbers . . . . . . . . 18--25
P. G. Garcia and
Steve Ligh A Generalization of Euler's $ \phi
$-Function . . . . . . . . . . . . . . . 26--28
C. Georghiou and
A. N. Philippou Harmonic Sums and the Zeta Function . . 29--36
Karel L. de Bouv\`ere and
Regina E. Lathrop Injectivity of Extended Generalized
Fibonacci Sequences . . . . . . . . . . 37--52
Clark Kimberling One-Free Zeckendorf Sums . . . . . . . . 53--57
Shmuel Zaks Generalized Profile Numbers . . . . . . 58--61
D. H. Lehmer and
Emma Lehmer Properties of Polynomials having
Fibonacci Numbers for Coefficients . . . 62--64
Ömer Egecio\uglu The Parity of the Catalan Number via
Lattice Paths . . . . . . . . . . . . . 65--66
A. P. Hillman Elementary Problems and Solutions . . . 67--73
Raymond E. Whitney Advanced Problems and Solutions . . . . 74--81
Andreas N. Philippou A Note on the Fibonacci Sequence of
Order $K$ and the Multinomial
Coefficients . . . . . . . . . . . . . . 82--86
E. Ehrhart Associated Hyperbolic and Fibonacci
Identities . . . . . . . . . . . . . . . 87--96
Wesley A. Darbro and
Georg von Tiesenhausen Sequences Generated by Self-Replicating
Systems . . . . . . . . . . . . . . . . 97--106
M. G. Monzingo Why are 8:18 and 10:09 Such Pleasant
Times? . . . . . . . . . . . . . . . . . 107--110
M. E. Cohen and
D. L. Hudson On Exponential Series Expansions and
Convolutions . . . . . . . . . . . . . . 111--117
Yasuichi Horibe Notes on Fibonacci Trees and Their
Optimality . . . . . . . . . . . . . . . 118--128
Robert D. Girse A Note on Fibonacci Cubature . . . . . . 129--131
O. R. Ainsworth and
J. Neggers A Family of Polynomials and Powers of
the Secant . . . . . . . . . . . . . . . 132--138
David R. Hale A Variant of Nim and a Function Defined
by Fibonacci Representation . . . . . . 139--142
Wayne M. Lawton Kronecker's Theorem and Rational
Approximation of Algebraic Numbers . . . 143--146
A. P. Hillman Elementary Problems and Solutions . . . 147--152
Raymond E. Whitney Advanced Problems and Solutions . . . . 153--161
S. N. Singh and
B. K. Rai Properties of Some Extended Bernoulli
and Euler Polynomials . . . . . . . . . 162--172
Wilhelm Werner Comment on Problem H-315 . . . . . . . . 173
David W. Bange and
Anthony E. Barkauskas Fibonacci Graceful Graphs . . . . . . . 174--188
Lee Erlebach and
William Yslas Vélez Equiprobability in the Fibonacci
Sequence . . . . . . . . . . . . . . . . 189--191
Sána Josef Lucas Triangle . . . . . . . . . . . . . 192--195
J. L. Hock and
R. B. McQuistan The Occupational Degeneracy for $
\lambda $-Bell Particles on a Saturated
$ \lambda \times N $ Lattice Space . . . 196--202
Narsingh Deo and
Michael Quinn Pascal Graphs and Their Properties . . . 203--214
Neville Robbins On Fibonacci Numbers Which are Powers:
II . . . . . . . . . . . . . . . . . . . 215--218
Peter Kirschenhofer and
Helmut Prodinger and
Robert F. Tichy Fibonacci Numbers of Graphs: II . . . . 219--228
B. H. Neumann and
L. G. Wilson Corrigenda to ``Some Sequences Like
Fibonacci's'' . . . . . . . . . . . . . 229
A. P. Hillman and
G. C. Padilla Elementary Problems and Solutions . . . 230--235
Raymond E. Whitney Advanced Problems and Solutions . . . . 236--241
V. R. R. Uppuluri and
S. A. Patil Waiting Times and Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 242--249
John H. Selleck Powers of $T$ and Soddy Circles . . . . 250--252
Gerhard Rosenberger On Some Divisibility Properties of
Fibonacci and Related Numbers . . . . . 253--258
John Brillhart Letter to the editor: ``Properties of
polynomials having Fibonacci numbers for
coefficients'' [Fibonacci Quart. \bf 21
(1983), no. 1, 62--64; MR 84f:10018a] by
D. H. Lehmer and E. Lehmer . . . . . . . 259--259
H. N. Malik On the Solution of $ \{ E^2 + (\lambda p
- 2) E + (1 - \lambda p - \lambda^2 q)
\}^m G_n = n^k $ by Expansions and
Operators . . . . . . . . . . . . . . . 260--265
Neville Robbins On Fibonacci Numbers of the Form $ P X^2
$, Where $P$ is Prime . . . . . . . . . 266--271
W. J. A. Colman A General Method for Determining a
Closed Formula for the Number of
Partitions of the Integer $n$ into $m$
Positive Integers for Small Values of
$m$ . . . . . . . . . . . . . . . . . . 272--284
Malvina Baica $n$-Dimensional Fibonacci Numbers and
Their Applications . . . . . . . . . . . 285--301
T. C. Wu Counting the Profiles in Domino Tiling 302--303
Karolyn A. Morgan The Fibonacci Sequence $ F_n $ Modulo $
L_m $ . . . . . . . . . . . . . . . . . 304--305
A. P. Hillman and
G. C. Padalla and
C. R. Wall Elementary Problems and Solutions . . . 306--311
Raymond E. Whitney Advanced Problems and Solutions . . . . 312--317
Anonymous Conference Announcement . . . . . . . . 318
Anonymous Volume Index . . . . . . . . . . . . . . 319
V. E. Hoggatt, Jr. and
Marjorie Bicknell-Johnson Additive Partition of the Positive
Integers and Generalized Fibonacci
Representations . . . . . . . . . . . . 2--21
Gerald E. Bergum Addenda to Geometry of a Generalized
Simson's Formula . . . . . . . . . . . . 22--28
Alain J. Phares General Solution of a Fibonacci-Like
Recursion Relation and Applications . . 29--41
Eduard Fuchs Partitions, Compositions and Cyclomatic
Number of Function Lattices . . . . . . 42--49
H. J. J. te Riele Rules for Constructing Hyperperfect
Numbers . . . . . . . . . . . . . . . . 50--60
S. Pethe On Lucas Polynomials and Some Summation
Formulas for Chebychev Polynomial
Sequences via Them . . . . . . . . . . . 61--69
Oreste W. Lombardi and
Margaret A. Lombardi The Golden Mean in the Solar System . . 70--75
Kenji Nagasaka Distribution Property of Recursive
Sequences Defined by $ u_{n + 1} \equiv
u_n + u_n^{-1} \pmod {m} $ . . . . . . . 76--81
Anonymous Fibonacci Research Conference
Announcement . . . . . . . . . . . . . . 82
Anonymous Acknowledgments . . . . . . . . . . . . 83
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 84--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--97
Lawrence Somer The Generation of Higher-Order Linear
Recurrences from Second-Order Linear
Recurrences . . . . . . . . . . . . . . 98--100
D. S. Meek and
G. H. J. Van Rees The Solution of an Iterated Recurrence 101--104
William I. McLaughlin and
Sylvia A. Lundy Digit Functions of Integer Sequences . . 105--115
Joseph J. Heed Wieferichs and the Problems $z(p^2) =
z(p)$ . . . . . . . . . . . . . . . . . 116--118
T. Cacoullos and
H. Papageorgiou Multiparameter Stirling and $C$-Numbers:
Recurrences and Applications . . . . . . 119--133
M. C. Er The Matrices of Fibonacci Numbers . . . 134--139
Peter Hagis, Jr. Lower Bounds for Unitary Multiperfect
Numbers . . . . . . . . . . . . . . . . 140--143
Peter H. St. John On the Asymptotic Proportions of Zeros
and Ones in Fibonacci Sequences . . . . 144--145
Richard C. Bollinger Fibonacci $k$-Sequences, Pascal-$T$
Triangles, and $k$-In-a-Row Problems . . 146--151
Kent D. Boklan The $n$-Number Game . . . . . . . . . . 152--155
F. T. Howard Weighted Associated Stirling Numbers . . 156--165
Nadhla A. Al-Salam Some Operational Formulas for the
$q$-Laguerre Polynomials . . . . . . . . 166--170
Fred Dodd The Number Field $ Q(\sqrt {5}) $ and
the Fibonacci Numbers . . . . . . . . . 171--177
Derek K. Chang A Note on Apery Numbers . . . . . . . . 178--180
Anonymous Fibonacci Research Conference
Announcement . . . . . . . . . . . . . . 181--182
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 183--187
Raymond E. Whitney Advanced Problems and Solutions . . . . 188--193
Ernst S. Selmer A Note on Somer's Paper on Linear
Recurrences . . . . . . . . . . . . . . 194--195
P. Ligomenides and
R. Newcomb Multilevel Fibonacci Conversion and
Addition . . . . . . . . . . . . . . . . 196--203
M. C. Er Sums of Fibonacci Numbers by Matrix
Methods . . . . . . . . . . . . . . . . 204--207
Gonzalo R. Arce Fibonacci and Related Sequences in
Digital Filtering . . . . . . . . . . . 208--217
E. Ehrhart Euler's Integers . . . . . . . . . . . . 218--228
Pin-Yen Lin The General Solution to the Decimal
Fraction of Fibonacci Series . . . . . . 229--234
Hugo S. Sun and
M. E. Cohen An Easy Proof of the Greenwood--Gleason
Evaluation of the Ramsey Number $ R(3,
3, 3) $ . . . . . . . . . . . . . . . . 235--238
A. G. Shannon Some Asymptotic Properties of
Generalized Fibonacci Numbers . . . . . 239--243
Ian Bruce A Modified Tribonacci Sequence . . . . . 244--246
A. G. Shannon and
A. F. Horadam and
Gerald E. Bergum Infinite Classes of Sequence-Generated
Circles . . . . . . . . . . . . . . . . 247--251
Naomi Levine The Goose That Laid the Golden Egg . . . 252--254
Glenn Hopkins and
William Staton Some Identities Arising from the
Fibonacci Numbers of Certain Graphs . . 255--258
Shiro Ando On the Numbers of the Form $ a n^2 + b n
$ . . . . . . . . . . . . . . . . . . . 259--260
Blagoj S. Popov On Certain Series of Reciprocals of
Fibonacci Numbers . . . . . . . . . . . 261--265
L. Carlitz An Application of the Reciprocity
Theorem for Dedekind Sums . . . . . . . 266--269
A. F. Horadam Coaxal Circles Associated with
Recurrence-Generated Sequences . . . . . 270--272
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 273--278
Raymond E. Whitney Advanced Problems and Solutions . . . . 279--289
C. S. Bisht Some Congruence Properties of
Generalized Lucas Integral Sequences . . 290--295
Ch. A. Charalambides On Weighted Stirling and Other Related
Numbers and Some Combinatorial
Applications . . . . . . . . . . . . . . 296--309
Peter J. Downey and
Ralph E. Griswold On a Family of Nested Recurrences . . . 310--317
Hartmut Höft and
Margret Höft An Order-Theoretic Representation of the
Polygonal Numbers . . . . . . . . . . . 318--323
A. F. Horadam Pell Numbers and Coaxal Circles . . . . 324--326
W. R. Spickerman and
R. N. Joyner Binet's Formula for the Recursive
Sequence of Order $K$ . . . . . . . . . 327--331
J. O. Shallit Some Predictable Pierce Expansions . . . 332--335
J. E. Walton and
A. F. Horadam Generalized Pell Polynomials and Other
Polynomials . . . . . . . . . . . . . . 336--339
Neville Robbins On Pell Numbers of the form $ P X^2 $,
Where $P$ is Prime . . . . . . . . . . . 340--348
Charles R. Wall A Fibonacci-Like Sequence of Abundant
Numbers . . . . . . . . . . . . . . . . 349
Ourania Chrysaphinou A Note on the Cycle Indicator . . . . . 350--353
Robert Schoen Harmonic, Geometric, and Arithmetic
Means in Generalized Fibonacci Sequences 354--357
M. J. DeLeon $n$ th Power Residues Congruent to One 358--364
Peter Hagis, Jr. and
Graham Lord Letter to the Editor . . . . . . . . . . 365
Charles R. Wall Response . . . . . . . . . . . . . . . . 365
J. O. Shallit and
J. P. Yamron On Linear Recurrences and Divisibility
by Primes . . . . . . . . . . . . . . . 366--368
A. P. Hillman and
Gloria C. Padilla Elementary Problems and Solutions . . . 369--373
Raymond E. Whitney Advanced Problems and Solutions . . . . 374--381
Anonymous Volume Index . . . . . . . . . . . . . . 382
Anonymous Acknowledgments . . . . . . . . . . . . 2
Karel Zikan and
Edward Schmeichel A Path Counting Problem in Digraphs . . 3--6
A. F. Horadam and
Bro. J. M. Mahon Pell and Pell--Lucas Polynomials . . . . 7--20
Krassimir T. Atanassov and
Liliya C. Atanassova and
Dimitar D. Sasselov A New Perspective to the Generalization
of the Fibonacci Sequence . . . . . . . 21--28
Günter Köhler Generating Functions of Fibonacci-Like
Sequences and Decimal Expansions of Some
Fractions . . . . . . . . . . . . . . . 29--35
S. P. Mohanty and
A. M. S. Ramasamy On $ P_{r, k} $ Sequences . . . . . . . 36--44
A. Kyriakoussis A Congruence for a Class of Exponential
Numbers . . . . . . . . . . . . . . . . 45--48
A. J. Stam Regeneration Points in Random
Permutations . . . . . . . . . . . . . . 49--56
S. Pethe On Lucas Fundamental Functions and
Chebychev Polynomial Sequences . . . . . 57--65
H. W. Gould and
W. E. Greig A Lucas Triangle Primality Criterion
Dual to that of Mann--Shanks . . . . . . 66--69
G. L. Cohen and
R. J. Williams Extensions of Some Results Concerning
Odd Perfect Numbers . . . . . . . . . . 70--76
Charles R. Wall On Triangular Fibonacci Numbers . . . . 77--79
Charles R. Wall Guessing Exact Solutions . . . . . . . . 80
Dorin Andrica and
Serban Buzeteanu On the Reduction of a Linear Recurrence
of Order $r$ . . . . . . . . . . . . . . 81--84
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 85--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--97
Karel L. de Bouv\`ere and
Herta T. Freitag First International Conference on
Fibonacci Numbers and Their
Applications: Two Reports . . . . . . . 98--99
Andreas N. Philippou and
Costas Georghiou and
George N. Philippou Fibonacci-Type Polynomials of Order $K$
with Probability Applications . . . . . 100--105
I. N. Baker and
P. J. Rippon A Note on Infinite Exponentials . . . . 106--112
Henry L. Alder and
Amin A. Muwafi and
Jeffrey K. Lewis Euler's Partition Identity --- Are There
Any More Like It? . . . . . . . . . . . 113--119
J. H. Clarke and
A. G. Shannon Some Generalized Lucas Sequences . . . . 120--125
P. Horák and
L. Skula A Characterization of the Second-Order
Strong Divisibility Sequences . . . . . 126--132
M. G. Monzingo On the Distribution of Consecutive
Triples of Quadratic Residues and
Quadratic Nonresidues and Related Topics 133--138
Charles Laywine and
Gary L. Mullen Latin Cubes and Hypercubes of Prime
Order . . . . . . . . . . . . . . . . . 139--145
R. M. Sternheimer A Corollary to Iterated Exponentiation 146--148
Blake Ralston Elemental Complete Composite Number
Generators . . . . . . . . . . . . . . . 149--150
Nicholas J. Rose A Note on a Fibonacci Identity . . . . . 151--152
Marshall Walker Golden Cuboid Sequences . . . . . . . . 153--154
Tony Van Ravenstein and
Graham Winley and
Keith Tognetti A Property of Convergents to Golden Mean 155--157
O. W. McClung Generators of Unitary Amicable Numbers 158--165
Mauro Boscarol A Note on Binomial Coefficients and
Chebyshev Polynomials . . . . . . . . . 166--168
R. Dawson and
G. Gabor and
R. Nowakowski and
D. Wiens Random Fibonacci-Type Sequences . . . . 169--176
P. W. Epasinghe Euclid's Algorithm and the Fibonacci
Numbers . . . . . . . . . . . . . . . . 177--179
Gerald E. Bergum Letter from the Editor . . . . . . . . . 180
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 181--185
Raymond E. Whitney Advanced Problems and Solutions . . . . 186--193
Vichian Laohakosol and
Nit Roenrom A Third-Order Analog of a Result of L.
Carlitz . . . . . . . . . . . . . . . . 194--198
Jannis A. Antoniadis Generalized Fibonacci Numbers and Some
Diophantine Equations . . . . . . . . . 199--213
A. F. Horadam Zigzag Polynomials . . . . . . . . . . . 214--220
Calvin T. Long On a Fibonacci Arithmetical Trick . . . 221--231
Hartmut Höft and
Margret Höft A Fibonacci Sequence of Distributive
Lattices . . . . . . . . . . . . . . . . 232--237
Blagoj S. Popov A Note on the Sums of Fibonacci and
Lucas Polynomials . . . . . . . . . . . 238--239
G. E. Bergum and
Larry Bennett and
A. F. Horadam and
S. D. Moore Jacobsthal Polynomials and a Conjecture
Concerning Fibonacci-Like Matrices . . . 240--248
F. T. Howard Integers Related to the Bessel Function
$ J_1 (z) $ . . . . . . . . . . . . . . 249--257
G. Baron and
F. T. Boesch and
H. Prodinger and
R. F. Tichy and
J. F. Wang The Number of Spanning Trees in the
Square of a Cycle . . . . . . . . . . . 258--264
Kenneth B. Stolarsky and
Steven Greenbaum A Ratio Associated with $ \Phi (x) = n $ 265--269
Walter E. Beck and
Rudolph M. Najar Hyperperfect and Unitary Hyperperfect
Numbers . . . . . . . . . . . . . . . . 270--275
Anonymous Announcement . . . . . . . . . . . . . . 276
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 277--281
Raymond E. Whitney Advanced Problems and Solutions . . . . 282--289
Claude Levesque On $m$-th Order Linear Recurrences . . . 290--293
A. F. Horadam Gegenbauer Polynomials Revisited . . . . 294--299
Jannis A. Antoniadis Fibonacci and Lucas Numbers of the Form
$ 3 z^2 + 1 $ . . . . . . . . . . . . . 300--307
Marjorie Bicknell-Johnson Generalized Wythoff Numbers form
Simultaneous Fibonacci Representations 308--318
Bro. J. M. Mahon and
A. F. Horadam Inverse Trigonometrical Summation
Formulas Involving Pell Polynomials . . 319--324
Georg Schrage A Two-Dimensional Generalization of
Grundy's Game . . . . . . . . . . . . . 325--329
Eric M. Neufeld and
Charles J. Colbourn Lucas Sequences in Subgraph Counts of
Series-Parallel and Related Graphs . . . 330--337
Andreas N. Philippou and
Frosso S. Makri Longest Success Runs and Fibonacci-Type
Polynomials . . . . . . . . . . . . . . 338--345
Anonymous Announcement . . . . . . . . . . . . . . 346
Marie-Louis Lavertu and
Claude Levesque On Bernstein's Combinatorial Identities 347--355
Craig A. Tovey Multiple Occurrences of Binomial
Coefficients . . . . . . . . . . . . . . 356--358
Michael Frenklach Linear Recurrence Relations with
Binomial Coefficients . . . . . . . . . 359--363
Hans Herda The Series of Prime Square Reciprocals 364--365
C. A. Church, Jr. Combinatorial Proof for a Sorting
Problem Identity . . . . . . . . . . . . 366--368
Arthur Barry and
Stanley Bezuszka, S. J. A Fibonacci and Lucas Tannenbaum . . . . 369--370
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 371--375
Raymond E. Whitney Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Talbot M. Katz and
Daniel I. A. Cohen The First Digit Property for Exponential
Sequences is Independent of the
Underlying Distribution . . . . . . . . 2--7
A. F. Horadam Generalized Zigzag Polynomials . . . . . 8--16
Blagoj S. Popov Summation of Reciprocal Series of
Numerical Functions of Second Order . . 17--21
J. O. Shallit Metric Theory of Pierce Expansions . . . 22--40
Michael Filaseta Newton's Method and Simple Continued
Fractions . . . . . . . . . . . . . . . 41--45
G. E. Bergum Letter from the Editor . . . . . . . . . 46
I. J. Good Skew Circulants and the Theory of
Numbers . . . . . . . . . . . . . . . . 47--60
J. C. Turner On a Class of Knots with Fibonacci
Invariant Numbers . . . . . . . . . . . 61--66
John A. Ewell On Two- and Four-Part Partitions of
Numbers Each Part a Square . . . . . . . 67--69
Dario Castellanos Rapidly Converging Expansions with
Fibonacci Coefficients . . . . . . . . . 70--82
Anonymous Announcement . . . . . . . . . . . . . . 83
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 84--87
Raymond E. Whitney Advanced Problems and Solutions . . . . 88--97
Anonymous Acknowledgements . . . . . . . . . . . . 98
Shoichi Hirose On Some Polygonal Numbers Which are, at
the Same Time, the Sums, Differences,
and Products of Two Other Polygonal
Numbers . . . . . . . . . . . . . . . . 99--105
O. William McClung Letter to the Editor . . . . . . . . . . 106
R. M. Sternheimer Some Results Concerning Pythagorean
Triplets . . . . . . . . . . . . . . . . 107--128
Werner Georg Nowak On the Minimum of a Ternary Cubic Form 129--132
Tad White On the Coefficients of a Recursion
Relation for the Fibonacci Partition
Function . . . . . . . . . . . . . . . . 133--137
Derek K. Chang Higher-Order Fibonacci Sequences Modulo
$M$ . . . . . . . . . . . . . . . . . . 138--139
Richard C. Bollinger A Note on Pascal-$T$ Triangles,
Multinomial Coefficients, and Pascal
Pyramids . . . . . . . . . . . . . . . . 140--143
Anonymous Research Conference Announcement . . . . 144
A. W. Goodman An Entire Function That Gives the
Fibonacci Numbers at the Integers . . . 145--149
John A. Ewell On the Enumerator for Sums of Three
Squares . . . . . . . . . . . . . . . . 150--153
Harlan R. Stevens Bernoulli Numbers and Kummer's Criterion 154--159
Calvin T. Long Discovering Fibonacci Identities . . . . 160--167
F. T. Howard Explicit Formulas for Numbers of
Ramanujan . . . . . . . . . . . . . . . 168--175
I. J. Good Skew Circulants and the Theory of
Numbers: An Addendum . . . . . . . . . . 176--177
Derek K. Chang On Fibonacci Binary Sequences . . . . . 178--179
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 180--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--193
James E. Desmond Expansion of the Fibonacci Numbers $
F_{m n + r} $ in the $m$ th Powers of
Fibonacci or Lucas Numbers . . . . . . . 194--208
Joseph W. Creely Some Combinatorial Sequences . . . . . . 209--220
A. F. Horadam Hypersurfaces Associated with Simson
Formula Analogues . . . . . . . . . . . 221--226
A. F. Horadam Determinantal Hypersurfaces for Lucas
Sequences of Order $r$, and a
Generalization . . . . . . . . . . . . . 227--237
E. J. Farrell On the Occurrences of Fibonacci
Sequences in the Counting of Matchings
in Linear Polygonal Chains . . . . . . . 238--246
J.-P. Gallinar The Fibonacci Ratio in a Thermodynamical
Problem: a Combinatorial Approach . . . 247--250
B. P. Sinha and
S. Ghose and
B. B. Bhattacharya and
P. K. Srimani A Further Note on Pascal Graphs . . . . 251--257
Derek K. Chang On Fibonacci $k$-ary Trees . . . . . . . 258--262
Dean S. Clark Fibonacci Numbers as Expected Values in
a Game of Chance . . . . . . . . . . . . 263--267
Ian Bruce Sequences Generated by Multiple
Reflections . . . . . . . . . . . . . . 268--272
Paul S. Bruckman A Relation for the Prime Distribution
Function . . . . . . . . . . . . . . . . 273--276
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 277--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--289
Bro. J. M. Mahon and
A. F. Horadam Matrix and Other Summation Techniques
for Pell Polynomials . . . . . . . . . . 290--308
Marjorie Bicknell-Johnson Letter to the Editor . . . . . . . . . . 309
Hugh M. Edgar On the Least Common Multiple of Some
Binomial Coefficients . . . . . . . . . 310--312
Clarence B. Larison Sidney's Series . . . . . . . . . . . . 313--315
Gert Almkvist A Solution to a Tantalizing Problem . . 316--322
J. M. H. Peters Tenth Roots and the Golden Ratio . . . . 323--327
G. L. Chia A Note Concerning the Number of
Odd-Order Magic Squares . . . . . . . . 328--331
H. T. Freitag and
G. M. Phillips A Congruence Relation for Certain
Recursive Sequences . . . . . . . . . . 332--335
Piero Filipponi A Note on the Representation of Integers
as a Sum of Distinct Fibonacci Numbers 336--343
A. F. Horadam and
A. P. Treweek Simson's Formula and an Equation of
Degree $ 24 $ . . . . . . . . . . . . . 344--346
Charles Vanden Eynden Differences between Squares and Powerful
Numbers . . . . . . . . . . . . . . . . 347--348
Calvin T. Long A Note on Moessner's Process . . . . . . 349--355
Howard J. Wilcox Fibonacci Sequences of Period $n$ in
Groups . . . . . . . . . . . . . . . . . 356--361
Krassimir T. Atanassov On a Second New Generalization of the
Fibonacci Sequence . . . . . . . . . . . 362--365
A. F. Horadam and
S. Pethe Euclidean Coordinates as Generalized
Fibonacci Numbers Products . . . . . . . 366--370
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 371--375
Raymond E. Whitney Advanced Problems and Solutions . . . . 376--381
R. Herz-Fischler Letter to the Editor . . . . . . . . . . 382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Marjorie Bicknell-Johnson A Short History of \booktitleThe
Fibonacci Quarterly . . . . . . . . . . 2--5
Peter Hagis, Jr. A Systematic Search for Unitary
Hyperperfect Numbers . . . . . . . . . . 6--10
Steven Kahan Cyclic Counting Trios . . . . . . . . . 11--20
Bro. J. M. Mahon and
A. F. Horadam Pell Polynomial Matrices . . . . . . . . 21--28
Neville Robbins Representing \binom(2n, n) as a Sum of
Squares . . . . . . . . . . . . . . . . 29--33
R. A. Mollin and
P. G. Walsh On Nonsquare Powerful Numbers . . . . . 34--37
W. J. A. Colman An Upper Bound for the General
Restricted Partition Problem . . . . . . 38--44
Bro. J. M. Mahon and
A. F. Horadam Ordinary Generating Functions for Pell
Polynomials . . . . . . . . . . . . . . 45--56
Peter M. Higgins The Naming of Popes and a Fibonacci
Sequence in Two Noncommuting
Indeterminates . . . . . . . . . . . . . 57--61
Richard T. Bumby Incredible Identities Revisited . . . . 62--64
W. Aiello and
G. E. Hardy and
M. V. Subbarao On the Existence of $e$-Multiperfect
Numbers . . . . . . . . . . . . . . . . 65--71
Jin-Zai Lee and
Jia-Sheng Lee A Complete Characterization of $B$-Power
Fractions That can be Represented as
Series of General $n$-Bonacci Numbers 72--75
Wayne L. McDaniel The Existence of Infinitely Many
$k$-Smith Numbers . . . . . . . . . . . 76--80
Peter R. J. Asveld A Family of Fibonacci-Like Sequences . . 81--83
Anonymous Referees . . . . . . . . . . . . . . . . 84
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 85--89
Raymond E. Whitney Advanced Problems and Solutions . . . . 90--97
Herta T. Freitag The Second International Conference on
Fibonacci Numbers and Their
Applications: a Memory-Laden Experience 98--99
A. G. Shannon A. F. Horadam --- Ad Multos Annos . . . 100--104
Anonymous Third International Conference
Announcement . . . . . . . . . . . . . . 105
Br. J. Mahon and
A. F. Horadam A Constellation of Sequences of
Generalized Pell Polynomials . . . . . . 106--110
Jin-Zai Lee and
Jia-Sheng Lee Some Properties of the Generalization of
the Fibonacci Sequence . . . . . . . . . 111--117
Philip G. Engstrom Sections, Golden and Not So Golden . . . 118--127
S. B. Nandi and
S. K. Dutta On Associated and Generalized Lah
Numbers and Applications to Discrete
Distributions . . . . . . . . . . . . . 128--136
Thomas P. Dence Ratios of Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 137--143
Peter Hagis, Jr. Bi-Unitary Amicable and Multiperfect
Numbers . . . . . . . . . . . . . . . . 144--150
Evdokia Xekalaki and
John Panaretos and
Andreas Philippou On Some Mixtures of Distributions of
Order $k$ . . . . . . . . . . . . . . . 151--160
Daniel A. Rawsthorne Counting the ``Good'' Sequences . . . . 161--162
Richard H. Hudson Convergence of Tribonacci Decimal
Expansions . . . . . . . . . . . . . . . 163--170
Graham Winley and
Keith Tognetti and
Tony van Ravenstein A Property of Numbers Equivalent to the
Golden Mean . . . . . . . . . . . . . . 171--173
Joseph W. Creely The Length of a Two-Number Game . . . . 174--179
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 180--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--193
Bro. J. M. Mahon and
A. F. Horadam Exponential Generating Functions for
Pell Polynomials . . . . . . . . . . . . 194--203
Michael E. Mays Iterating the Division Algorithm . . . . 204--213
R. B. McNeill A Note on Divisibility Sequences . . . . 214--215
J. M. Metzger and
S. P. Kaler A Note on the Pell Equation . . . . . . 216--220
Lawrence Somer On $r$ th-Order Recurrences . . . . . . 221--224
Wayne L. McDaniel Powerful $k$-Smith Numbers . . . . . . . 225--228
Clement Frappier On the Derivatives of Composite
Functions . . . . . . . . . . . . . . . 229--239
Thomas H. Hildebrandt Letter to the Editor . . . . . . . . . . 240
László Tóth A Note on a Generalization of Euler's $
\Phi $ Function . . . . . . . . . . . . 241--243
Anonymous Third International Conference
Announcement . . . . . . . . . . . . . . 244
James C. Owings, Jr. Solution of the System $ a^2 \equiv - 1
\pmod {b} $, $ b^2 \equiv - 1 \pmod {a}
$ . . . . . . . . . . . . . . . . . . . 245--249
Sajal D. Das and
Narsingh Deo Rencontres Graphs: a Family of
Bipartitie Graphs . . . . . . . . . . . 250--262
Anne L. Ludington Transposable Integers in Arbitrary Bases 263--267
Jin-Zai Lee and
Jia-Sheng Lee Some Properties of the Sequence $ \{
W_n(a, b; p, q) \} $ . . . . . . . . . . 268--278
A. P. Hillman and
Gloria C. Padilla and
Charles R. Wall Elementary Problems and Solutions . . . 279--283
Raymond E. Whitney Advanced Problems and Solutions . . . . 284--289
Anonymous Third Annual Conference Announcement . . 290
A. F. Horadam and
Bro. J. M. Mahon Mixed Pell Polynomials . . . . . . . . . 291--299
Karl Dilcher A Generalization of Fibonacci
Polynomials and a Representation of
Gegenbauer Polynomials of Integer Order 300--303
F. T. Howard The Reciprocal of the Bessel Function $
J_k(z) $ . . . . . . . . . . . . . . . . 304--311
Charles R. Wall On the Largest Odd Component of a
Unitary Perfect Number . . . . . . . . . 312--316
A. K. Agarwal A Note on $ n(x, y) $-Reflected Lattice
Paths . . . . . . . . . . . . . . . . . 317--319
N. Balasubrahmanyan and
R. Sivaramakrishnan Friendly-Pairs of Multiplicative
Functions . . . . . . . . . . . . . . . 320--321
V. E. Hoggatt, Jr. and
M. A. Owens Hoggatt Sequences and Lexicographic
Ordering . . . . . . . . . . . . . . . . 322--332
Steve Ligh and
Charles R. Wall Functions of Non-Unitary Divisors . . . 333--338
Jin-Zai Lee and
Jia-Sheng Lee Some Properties of Binomial Coefficients 339--342
Charles R. Wall Analogs of Smith's Determinant . . . . . 343--345
L. C. Hsu Generalized Stirling Number Pairs
Associated with Inverse Relations . . . 346--351
Allan M. Krall and
Lance L. Littlejohn A Curious Set of Numbers . . . . . . . . 352--355
G. V. Milovanovi\'c and
G. Djordjevi\'c On Some Properties of Humbert's
Polynomials . . . . . . . . . . . . . . 356--360
Peter R. J. Asveld Another Family of Fibonacci-Like
Sequences . . . . . . . . . . . . . . . 361--364
Sharon Kunoff $ N! $ has the First Digit Property . . 365--367
Jia-Sheng Lee The $K$ th-Order Analog of a Result of
L. Carlitz . . . . . . . . . . . . . . . 368--369
A. P. Hillman Elementary Problems and Solutions . . . 370--375
Raymond E. Whitney Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Third International Conference
Announcement . . . . . . . . . . . . . . 2
A. F. Horadam and
A. G. Shannon Fibonacci and Lucas Curves . . . . . . . 3--13
Jin-Zai Lee and
Jia-Sheng Lee A Note on the Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 14--19
S. Pethe and
A. F. Horadam Generalized Gaussian Lucas Primordial
Functions . . . . . . . . . . . . . . . 20--30
M. G. Monzingo On Prime Divisors of Sequences of
Integers Involving Squares . . . . . . . 31--32
Yasuyuki Imai and
Yasuo Seto and
Shotaro Tanaka and
Hiroshi Yutani An Expansion of $ x^m $ and Its
Coefficients . . . . . . . . . . . . . . 33--39
Douglas Bowman A New Generalization of Davison's
Theorem . . . . . . . . . . . . . . . . 40--45
R. A. Mollin Generalized Fibonacci Primitive Roots,
and Class Numbers of Real Quadratic
Fields . . . . . . . . . . . . . . . . . 46--53
W. J. A. Colman On Certain Semi-Perfect Cuboids . . . . 54--57
Anne L. Ludington Generalized Transposable Integers . . . 58--63
Kung-Wei Yang Limits of $q$-Polynomial Coefficients 64--69
Bjorn Poonen Periodicity of a Combinatorial Sequence 70--76
A. F. Horadam Jacobsthal and Pell Curves . . . . . . . 77--83
Anonymous Referees . . . . . . . . . . . . . . . . 84
A. P. Hillman Elementary Problems and Solutions . . . 85--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--97
A. F. Horadam Elliptic Functions and Lambert Series in
the Summation of Reciprocals in Certain
Recurrence-Generated Sequences . . . . . 98--114
Piero Filipponi and
A. F. Horadam A Matrix Approach to Certain Identities 115--126
Peter Kiss On the Number of Solutions of the
Diophantine Equation $ \binom (x, p) =
\binom (y, 2) $ . . . . . . . . . . . . 127--129
Anonymous Third International Conference
Announcement . . . . . . . . . . . . . . 130
Pin-Yen Lin De Moivre-Type Identities for the
Tribonacci Numbers . . . . . . . . . . . 131--134
Yasuichi Horibe Entropy of Terminal Distributions and
the Fibonacci Trees . . . . . . . . . . 135--140
Joseph W. Creely The Length of a Three-Number Game . . . 141--143
S. Pethe Some Identities for Tribonacci Sequences 144--151
A. Zulauf and
J. C. Turner Fibonacci Sequences of Sets and Their
Duals . . . . . . . . . . . . . . . . . 152--156
L. Kuipers and
J.-S. Shiue On the $ L^p $-Discrepancy of Certain
Sequences . . . . . . . . . . . . . . . 157--162
Curtis N. Cooper and
Robert E. Kennedy A Partial Asymptotic Formula for the
Niven Numbers . . . . . . . . . . . . . 163--168
R. B. McNeill On Certain Divisibility Sequences . . . 169--171
William C. Waterhouse Integral $4$ by $4$ Skew Circulants . . 172--177
R. M. Sternheimer On a Result Involving Iterated
Exponentiation . . . . . . . . . . . . . 178--180
A. P. Hillman Elementary Problems and Solutions . . . 181--185
Raymond E. Whitney Advanced Problems and Solutions . . . . 186--193
Anonymous A Tribute to Brother Alfred Brousseau 194
Anne L. Ludington Length of the $7$-Number Game . . . . . 195--204
John C. Turner On Folyominoes and Feudominoes . . . . . 205--218
A. G. Shannon and
A. F. Horadam Generalized Fibonacci Continued
Fractions . . . . . . . . . . . . . . . 219--223
Morris Jack DeLeon Carlitz Four-Tuples . . . . . . . . . . 224--232
J. C. Turner Fibonacci Word Patterns and Binary
Sequences . . . . . . . . . . . . . . . 233--246
Gerhard Larcher A New Extremal Property of the Fibonacci
Ratio . . . . . . . . . . . . . . . . . 247--255
Jukka Pihko On Fibonacci and Lucas Representations
and a Theorem of Lekkerkerker . . . . . 256--261
Douglas Hensley A Winning Strategy at Taxman . . . . . . 262--270
Eugene Ehrhart On Prime Numbers . . . . . . . . . . . . 271--274
P. J. McCarthy A Generalization of Metrod's Identity 275--277
A. P. Hillman Elementary Problems and Solutions . . . 278--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--288
Herta T. Freitag A Report on the Third International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 289
Doug Wiedemann An Iterated Quadratic Extension of GF(2) 290--295
H. C. Williams A Note on the Primality of $ 6^{2^n} + 1
$ and $ 10^{2^n} + 1 $ . . . . . . . . . 296--305
Shari Lynn Levine Suppose More Rabbits are Born . . . . . 306--311
Charles R. Wall New Unitary Perfect Numbers have at
Least Nine Odd Components . . . . . . . 312--317
Renato M. Capocelli A Note on Fibonacci Trees and the
Zeckendorf Representation of Integers 318--324
Pentti Haukkanen A Note on Specially Multiplicative
Arithmetic Functions . . . . . . . . . . 325--327
Alvin Tirman and
T. Henry Jablonski, Jr. Identities Derived on a Fibonacci
Multiplication Table . . . . . . . . . . 328--331
John A. Ewell On Sums of Three Triangular Numbers . . 332--335
Andrzej Makowski Stroeker's Equation and Fibonacci
Numbers . . . . . . . . . . . . . . . . 336--337
W. J. A. Colman Some Observations on the Classical
Cuboid and Its Parametric Solutions . . 338--343
Paul Duvall and
Theresa Vaughan Pell Polynomials and a Conjecture of
Mahon and Horadam . . . . . . . . . . . 344--353
John C. Turner Convolution Trees and Pascal-$T$
Triangles . . . . . . . . . . . . . . . 354--365
Pavel Horák A Note on the Third-Order Strong
Divisibility Sequences . . . . . . . . . 366--371
A. P. Hillman Elementary Problems and Solutions . . . 372--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--381
Anonymous Book Review: \booktitleThe Book of
Squares . . . . . . . . . . . . . . . . 382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Leon Bernstein On Primitive Pythagorean Triangles with
Equal Perimeters . . . . . . . . . . . . 2--6
Krassimir T. Atanassov On a Generalization of the Fibonacci
Sequence in the Case of Three Sequences 7--10
Amos Ehrlich On the Periods of the Fibonacci Sequence
Modulo $m$ . . . . . . . . . . . . . . . 11--13
Daniel A. Rawsthorne How Many $1$'s Are Needed? . . . . . . . 14--17
Tony van Ravenstein Optimal Spacing of Points on a Circle 18--24
Lawrence Somer Congruence Relations for $k$ th-Order
Linear Recurrences . . . . . . . . . . . 25--30
Anonymous Referees . . . . . . . . . . . . . . . . 31--32
Robert A. Sulanke A Recurrence Restricted by a Diagonal
Condition: Generalized Catalan Arrays 33--46
John F. Morrison Fibonacci-Like Matrices . . . . . . . . 47--48
Arnold Knopfmacher and
John Knopfmacher Representations for Real Numbers via $k$
th Powers of Integers . . . . . . . . . 49--60
F. T. Howard and
E. K. Hayashi Congruences for Numbers of Ramanujan . . 61--69
Alejandro Necochea and
Larry Bennett On a Certain Sequence of Quotients of a
Sequence . . . . . . . . . . . . . . . . 70--75
J. C. Turner The Alpha and the Omega of the Wythoff
Pairs . . . . . . . . . . . . . . . . . 76--86
A. P. Hillman Elementary Problems and Solutions . . . 87--91
Raymond E. Whitney Advanced Problems and Solutions . . . . 92--97
Luo Ming On Triangular Fibonacci Numbers . . . . 98--108
Frank S. Gillespie A Generalization of Fermat's Little
Theorem . . . . . . . . . . . . . . . . 109--115
Bau-Sen Du A Simple Method which Generates
Infinitely Many Congruence Identities 116--123
Anonymous Announcement on Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 124
Padmavathamma On Andrews' Generalized Frobenius
Partitions . . . . . . . . . . . . . . . 125--130
Paul Duvall and
Theresa P. Vaughan Recursions for Carlitz Triples . . . . . 131--138
Robert E. Kennedy and
Curtis N. Cooper Niven Repunits and $ 10^n \equiv 1 \pmod
{n} $ . . . . . . . . . . . . . . . . . 139--143
Rudolph M. Najar Operations on Generators of Unitary
Amicable Pairs . . . . . . . . . . . . . 144--152
László Cseh and
Imre Merényi Recurrence Relations for a Power Series 153--155
C. Georghiou On Some Second-Order Linear Recurrences 156--159
Daniel C. Fielder and
Cecil O. Alford On a Conjecture by Hoggatt with
Extensions to Hoggatt Sums and Hoggatt
Triangles . . . . . . . . . . . . . . . 160--168
A. K. Agarwal Properties of a Recurring Sequences . . 169--175
L. Tóth and
J. Sándor An Asymptotic Formula Concerning a
Generalized Euler Function . . . . . . . 176--180
A. P. Hillman Elementary Problems and Solutions . . . 181--185
Jeffrey Shallit Letter to the Editor . . . . . . . . . . 186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
Selmo Tauber Some New Results on Quasi-Orthogonal
Numbers . . . . . . . . . . . . . . . . 194--200
Bruce E. Sagan and
Yeong-Nan Yeh Probabilistic Algorithms for Trees . . . 201--207
Anonymous Announcement: Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 208
Andreas N. Philippou and
Costas Georghiou Convolutions of Fibonacci-Type
Polynomials of Order $K$ and the
Negative Binomial Distributions of the
Same Order . . . . . . . . . . . . . . . 209--216
Y. H. Harris Kwong Minimum Periods of $ S(n, k) $ Modulo
$M$ . . . . . . . . . . . . . . . . . . 217--220
François Dubeau On $r$-Generalized Fibonacci Numbers . . 221--228
John C. Turner Note on a Family of Fibonacci-Like
Sequences . . . . . . . . . . . . . . . 229--231
Adina Di Porto and
Piero Filipponi Note on the Fibonacci Pseudoprimes . . . 232--241
J. W. Sander A Remark on a Theorem of Weinstein . . . 242--246
A. F. Alameddine Fibonacci Numbers and Bipyramids . . . . 247--252
Andrew Granville On a Class of Determinants . . . . . . . 253--256
Joseph W. Creely Generating Partitions Using a Modified
Greedy Algorithm . . . . . . . . . . . . 257--258
Irving Adler Concerning the Divisors of $N$ and the
Exponents They Belong to Modulo $ (N -
1) $ or $ (N + 1) $ . . . . . . . . . . 259--266
Jeffrey A. Brooks A General Recurrence Relation for
Reflections in Multiple Glass Plates . . 267--271
Richard C. Bollinger The Mann--Shanks Primality Criterion in
the Pascal-$T$ Triangle $ T_3 $ . . . . 272--275
Herta T. Freitag and
Piero Filipponi On the $F$-Representation of Integral
Sequences $ \{ F^2_n / d \} $ and $ \{
L^2_n / d \} $ Where $d$ is Either a
Fibonacci or a Lucas Number . . . . . . 276--282
H. W. Corley The Convolved Fibonacci Equation . . . . 283--284
G. L. Cohen and
S. L. Segal A Note Concerning Those $n$ for Which $
\Phi (n) + 1 $ Divides $n$ . . . . . . . 285--286
Vamsi Krishna Mootha and
George Berzsenyi Characterizations and Extendibility of $
P_t $-Sets . . . . . . . . . . . . . . . 287--289
Thomas E. Moore Euclid's Algorithm and Lamé's Theorem on
a Microcomputer . . . . . . . . . . . . 290--295
J. Arkin and
D. C. Arney and
G. E. Bergum and
S. A. Vurr and
B. J. Porter Unique Fibonacci Formulas . . . . . . . 296--302
Peter R. J. Asveld Fibonacci-Like Differential Equations
with a Polynomial Nonhomogeneous Part 303--309
Aleck J. Hunter and
M. Kovarik Integral Triangles and Circles . . . . . 310--315
Anonymous Announcement: Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 316
S. W. Graham Unitary Perfect Numbers with Squarefree
Odd Part . . . . . . . . . . . . . . . . 317--322
J. Arkin and
D. C. Arney and
G. E. Bergum and
S. A. Burr and
B. J. Porter Recurring-Sequence Tiling . . . . . . . 323--332
Sahib Singh A Diophantine Equation with
Generalization . . . . . . . . . . . . . 333--334
Eliot Jacobson Almost Uniform Distribution of the
Fibonacci Sequence . . . . . . . . . . . 335--337
Paul S. Bruckman The Generalized Zeckendorf Theorems . . 338--347
Y. H. Harris Kwong Minimum Periods of Binomial Coefficients
Modulo $M$ . . . . . . . . . . . . . . . 348--351
Peter C. Fishburn and
Andrew M. Odlyzko and
Fred S. Roberts Two-Sided Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 352--361
H. W. Gould Equivalence of Piza's Primality
Criterion with that of Gould--Greig and
Its Dual Relationship to the
Mann--Shanks Criterion . . . . . . . . . 362--365
V. Siva Rama Prasad and
M. V. S. Bhramarambica On the Schnirelmann Density of $M$-Free
Integers . . . . . . . . . . . . . . . . 366--368
Harry D'Souza Trapping a Real Number between Adjacent
Rationals . . . . . . . . . . . . . . . 369--371
Doron Zeilberger A Combinatorial Problem that Arose in
Biophysics . . . . . . . . . . . . . . . 372
A. P. Hillman Elementary Problems and Solutions . . . 373--377
Raymond E. Whitney Advanced Problems and Solutions . . . . 378--385
Pierre Damphousse The Arithmetic of Powers and Roots in $
G l_2 (C) $ and $ S l_2 (C) $ . . . . . 386--401
N. Gauthier Derivation of a Formula for $ \sum r^k
x^r $ . . . . . . . . . . . . . . . . . 402--407
Anonymous Announcement: Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 408
Eric Schissel Characterizations of Three Types of
Completeness . . . . . . . . . . . . . . 409--419
Graham Winley and
Keith Tognetti and
Tony van Ravenstein Hurwitz's Theorem and the Continued
Fraction with Constant Terms . . . . . . 420--423
Dario Castellanos A Generalization of Binet's Formula and
Some of Its Consequences . . . . . . . . 424--438
J. C. Turner and
A. G. Shannon On $K$ th-Order Colored Convolution
Trees and a Generalized Zeckendorf
Integer Representation Theorem . . . . . 439--447
Marjorie Bicknell-Johnson Retrograde Renegades and the Pascal
Connection: Repeating Decimals
Represented by Fibonacci and Other
Sequences Appearing from Right to Left 448--457
Ernest J. Eckert and
Preben Dahl Vestergaard Groups of Integral Triangles . . . . . . 458--464
Amitabha Tripathi A Box Filling Problem . . . . . . . . . 465--466
A. P. Hillman Elementary Problems and Solutions . . . 467--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473--478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
Br. J. M. Mahon and
A. F. Horadam Third-Order Diagonal Functions of Pell
Polynomials . . . . . . . . . . . . . . 3--10
Peter Hagis, Jr. Odd Nonunitary Perfect Numbers . . . . . 11--14
Anonymous Announcement: Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 15
Esayas George Kundert A Von Staudt--Clausen Theorem for
Certain Bernoullianlike Numbers and
Regular Primes of the First and Second
Kind . . . . . . . . . . . . . . . . . . 16--21
Clark Kimberling Fibonacci Hyperbolas . . . . . . . . . . 22--27
Derek K. Chang On Circular Fibonacci Binary Sequences 28--30
Supriya Mohanty and
S. P. Mohanty Pythagorean Numbers . . . . . . . . . . 31--42
N. Balasubramanian On Friendly-Pairs of Arithmetic
Functions . . . . . . . . . . . . . . . 43--47
Lee Knisley Sanders A Proof from Graph Theory for a
Fibonacci Identity . . . . . . . . . . . 48--55
M. G. Monzingo On the Sum $ \sum_{a = 1}^{p - 1} (a /
p)a $ . . . . . . . . . . . . . . . . . 56--59
Dan Kalman Sums of Powers by Matrix Methods . . . . 60--71
Konrad Engel On the Fibonacci Number of an $ M \times
N $ Lattice . . . . . . . . . . . . . . 72--78
J. W. Sander On Fibonacci Primitive Roots . . . . . . 79--80
Ivan Gutman and
Sven J. Cyvin A Result on $1$-Factors Related to
Fibonacci Numbers . . . . . . . . . . . 81--84
A. P. Hillman Elementary Problems and Solutions . . . 85--89
A. F. Horadam and
J. Lahr Letter to the Editor . . . . . . . . . . 90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Charles R. Wall Terminating Decimals in the Cantor
Ternary Set . . . . . . . . . . . . . . 98--101
Mark Nodine Note on the Resistance through a Static
Carry Look-Ahead Gate . . . . . . . . . 102--106
Marjorie Bicknell-Johnson Divisibility Properties of the Fibonacci
Numbers Minus One, Generalized to $ C_n
= C_{n - 1} + C_{n - 2} + k $ . . . . . 107--112
J. H. E. Cohn Palindromic Differences . . . . . . . . 113--120
Karen Anne Johnson A Hypercube Problem . . . . . . . . . . 121--128
Pin-Yen Lin Repeating Decimals Represented by
Tribonacci Sequences Appearing from Left
to Right or from Right to Left . . . . . 129--139
Anonymous Book Review: \booktitleA new chapter for
Pythagorean triples, by A. G. Schaake
and J. C. Turner . . . . . . . . . . . . 140, 155
Leon J. Lander Equal Sums of Unlike Powers . . . . . . 141--150
Stanley Bezuszka and
Stephen Kokoska A Polynomial Formula for Fibonacci
Numbers . . . . . . . . . . . . . . . . 151--155
P. R. Subramanian Springs of the Hermite Polynomials . . . 156--161
Patricia Jones On the Equation $ \phi $ (x) + $ \phi $
(k) = $ \phi $ (x+k) . . . . . . . . . . 162--165
H. W. Gould Series Transformations for Finding
Recurrences for Sequences . . . . . . . 166--171
Istvan Beck Partial Orders and the Fibonacci Numbers 172--174
Kevin Burrage Generalized Fibonacci Polynomials and
the Functional Iteration of Rational
Functions of Degree One . . . . . . . . 175--180
M. G. Monzingo On Certain Divisibility Sequences . . . 181
A. P. Hillman Elementary Problems and Solutions . . . 182--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--191
Anonymous Announcement of Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 192--193
A. K. Agarwal On a New Kind of Numbers . . . . . . . . 194--199
Henry Ibstedt Some Sequences of Large Integers . . . . 200--203
Tony van Ravenstein and
Graham Winley and
Keith Tognetti Characteristics and the Three Gap
Theorem . . . . . . . . . . . . . . . . 204--213
Anonymous Announcement: Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 214
Christian Krattenthaler A Two-Variable Lagrange-Type Inversion
Formula with Applications to Expansion
and Convolution Identities . . . . . . . 215--222
R. André-Jeannin Lambert Series and the Summation of
Reciprocals in Certain
Fibonacci--Lucas-Type Sequences . . . . 223--226
Eliot Jacobson The Distribution of Residues of Two-Term
Recurrence Sequences . . . . . . . . . . 227--229
J. C. Turner and
T. D. Robb Generalizations of the Dual Zeckendorf
Integer Representation Theorems ---
Discovery by Fibonacci Trees and Word
Patterns . . . . . . . . . . . . . . . . 230--239
Phillip G. Bradford The Fibonacci Sequence and the Time
Complexity of Generating the Conway
Polynomial and Related Topological
Invariants . . . . . . . . . . . . . . . 240--251
W. C. Chu An Algebraic Identity and Some Partial
Convolutions . . . . . . . . . . . . . . 252--254
J. Sándor and
L. Tóth On Certain Number-Theoretic Inequalities 255--258
Anne Ludington-Young Length of the $n$-Number Game . . . . . 259--265
J. Arkin and
D. C. Arney and
G. E. Bergum and
S. A. Burr and
B. J. Porter Tiling the $k$ th Power of a Power
Series . . . . . . . . . . . . . . . . . 266--272
Sahib Singh On a Hoggatt--Bergum Paper with Totient
Function Approach for Divisibility and
Congruence Relations . . . . . . . . . . 273--276
A. P. Hillman Elementary Problems and Solutions . . . 277--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--289
Arnold Knopfmacher A Radix Product Representation for Real
Numbers . . . . . . . . . . . . . . . . 290--297
E. E. Guerin Partitions with ``$ M(a) $ Copies of
$a$'' . . . . . . . . . . . . . . . . . 298--301
Amos Ehrlich Periods in Ducci's $n$-Number Game of
Differences . . . . . . . . . . . . . . 302--305
Neville Robbins Fibonacci Numbers of the Form $ C X^2 $,
Where $ 1 \leq C \leq 1000 $ . . . . . . 306--315
Pentti Haukkanen Vinogradov's Inversion Theorem for
Generalized Arithmetical Functions . . . 316--320
M. Koutras Two Classes of Numbers Appearing in the
Convolution of Binomial-Truncated
Poisson and Poisson-Truncated Binomial
Random Variables . . . . . . . . . . . . 321--333
Jon T. Butler On teh Number of Propagation Paths in
Multilayer Media . . . . . . . . . . . . 334--339
Kenji Nagasaka and
Jau-Shyong Shiue Asymptotic Positiveness of Linear
Recurrence Sequences . . . . . . . . . . 340--346
Adino Di Porto and
Piero Filipponi and
Emilio Montolivo On the Generalized Fibonacci
Pseudoprimes . . . . . . . . . . . . . . 347--353
Herta T. Freitag Report on the Fourth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 354
F. T. Howard Extensions of Congruences of Glaisher
and Nielsen Concerning Stirling Numbers 355--362
P. J. McCarthy and
R. Sivaramakrishnan Generalized Fibonacci Sequences via
Arithmetical Functions . . . . . . . . . 363--370
A. P. Hillman Elementary Problems and Solutions . . . 371--375
Raymond E. Whitney Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 384
Anonymous Referees . . . . . . . . . . . . . . . . 2
Joseph E. Carroll and
Ken Yanosko The Determination of a Class of
Primitive Integral Triangles . . . . . . 3--6
Ratko Tosic and
Olga Bodroza An Algebraic Expression for the Number
of Kekulé Structures of Benzenoid Chains 7--12
Richard André-Jeannin Generalized Complex Fibonacci and Lucas
Functions . . . . . . . . . . . . . . . 13--18
John Slivka and
Norman C. Severo Measures of Sets Partitioning Borel's
Simple Normal Numbers to Base $2$ in $
[0, 1] $ . . . . . . . . . . . . . . . . 19--22
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 23
Wayne L. McDaniel The G.C.D. in Lucas Sequences and Lehmer
Number Sequences . . . . . . . . . . . . 24--29
J. H. E. Cohn Recurrent Sequences Including $N$ . . . 30--36
Dixon J. Jones Continued Powers and Roots . . . . . . . 37--46
A. G. Shannon and
A. F. Horadam Generalized Staggered Sums . . . . . . . 47--51
Allen R. Miller Solutions of Fermat's Last Equation in
Terms of Wright's Hypergeometric
Function . . . . . . . . . . . . . . . . 52--56
Dario Castellanos A Generalization of a Result of Shannon
and Horadam . . . . . . . . . . . . . . 57--58
Richard J. Moll and
Shankar M. Venkatesan Fibonacci Numbers are not Context-Free 59--61
Krystyna Bialek and
Aleksander Grytczuk On Fermat's Equation . . . . . . . . . . 62--65
Bui Minh Phong Lucas Primitive Roots . . . . . . . . . 66--71
Lawrence Somer Distribution of Residues of Certain
Second-Order Linear Recurrences Modulo
$p$ --- II . . . . . . . . . . . . . . . 72--78
Kenneth S. Davis and
William A. Webb Pascal's Triangle Modulo $4$ . . . . . . 79--83
A. P. Hillman Elementary Problems and Solutions . . . 84--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--97
Dario Castellanos A Note on Bernoulli Polynomials . . . . 98--102
A. F. Horadam Fibonacci's Mathematical Letter to
Master Theodorus . . . . . . . . . . . . 103--107
Supriya Mohanty On Multi-Sets . . . . . . . . . . . . . 108--113
V. Giambalvo and
Ray Mines and
David J. Pengelley $p$-Adic Congruences Between Binomial
Coefficients . . . . . . . . . . . . . . 114--119
Clark Kimberling Zeckendorf Number Systems and Associated
Partitions . . . . . . . . . . . . . . . 120--123
Shmuel T. Klein Combinatorial Representation of
Generalized Fibonacci Numbers . . . . . 124--131
Richard André-Jeannin A Note on the Irrationality of Certain
Lucas Infinite Series . . . . . . . . . 132--135
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 136
A. K. Agarwal Combinatorial Interpretations of the
$q$-Analogues of $ L_{2 n + 1} $ . . . . 137--140
John Konvalina and
Yi-Hsin Liu Subsets Without Unit Separation and
Products of Fibonacci Numbers . . . . . 141--144
Robert E. Kennedy and
Curtis N. Cooper An Extension of a Theorem by Cheo and
Yien Concerning Digital Sums . . . . . . 145--149
Karl Dilcher Zeros of Certain Cyclotomy-Generated
Polynomials . . . . . . . . . . . . . . 150--156
Tom C. Brown and
Allen R. Freedman Some Sequences Associated with the
Golden Ratio . . . . . . . . . . . . . . 157--159
Kung-Wei Yang $q$-Determinants and Permutations . . . 160--163
Alwyn F. Horadam and
Piero Filipponi Cholesky Algorithm Matrices of Fibonacci
Type and Properties of Generalized
Sequences . . . . . . . . . . . . . . . 164--173
Timothy Chow A New Characterization of the
Fibonacci-Free Partition . . . . . . . . 174--179
Anonymous Elementary Problems Editor Retires . . . 180
A. P. Hillman Elementary Problems and Solutions . . . 181--185
Raymond E. Whitney Advanced Problems and Solutions . . . . 186--193
Clark Kimberling Second-Order Recurrence and Iterates of
$ [a n + 1 / 2] $ . . . . . . . . . . . 194--196
David Englund Entry Point Reciprocity of
Characteristic Conjugate Generalized
Fibonacci Sequences . . . . . . . . . . 197--198
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 199
Richard André-Jeannin Summation of Certain Reciprocal Series
Related to Fibonacci and Lucas Numbers 200--204
Richard André-Jeannin Sequences of Integers Satisfying
Recurrence Relations . . . . . . . . . . 205--208
Steven R. Finch Conjectures about $s$-Additive Sequences 209--214
Nenad Caki\'c A Note on Euler's Numbers . . . . . . . 215--216
Martin Bunder and
Keith Tognetti The Zeckendorf Representation and the
Golden Sequence . . . . . . . . . . . . 217--219
R. A. Bateman and
E. A. Clark and
M. L. Hancock and
C. A. Reiter The Period of Convergents Modulo $M$ of
Reduced Quadratic Irrationals . . . . . 220--229
Rita Giuliano Antonini On the Notion of Uniform Distribution
Mod $1$ . . . . . . . . . . . . . . . . 230--234
R. N. Whitaker and
A. G. Shannon Some Recursive Asymptotes . . . . . . . 235--238
Calvin Long and
John Bradshaw Second-Order Recurrences and the
Schröder--Bernstein Theorem . . . . . . . 239--243
Clark Kimberling Sets of Terms that Determine all the
Terms of a Linear Recurrence Sequence 244--248
Neville Robbins Some Convolution-Type and Combinatorial
Identities Pertaining to Binary Linear
Recurrences . . . . . . . . . . . . . . 249--255
Piero Filipponi A Note on a Class of Lucas Sequences . . 256--263
Bruce M. Landman and
Raymond N. Greenwell Multiplicative Partitions of Bipartite
Numbers . . . . . . . . . . . . . . . . 264--267
John Konvalina and
Yi-Hsin Liu A Combinatorial Interpretation of the
Square of a Lucas Number . . . . . . . . 268--270
Scott J. Beslin Reciprocal GCD Matrices and LCM Matrices 271--274
Herb Silverman Summing Infinite Series with Sex . . . . 275--276
Stanley Rabinowitz Elementary Problems and Solutions . . . 277--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--289
Ch. A. Charalambides Lucas Numbers and Polynomials of Order
$K$ and the Length of the Longest
Circular Success Run . . . . . . . . . . 290--297
Franz Halter-Koch Continued Fractions of Given Symmetric
Period . . . . . . . . . . . . . . . . . 298--303
Richard André-Jeannin On Determinants Whose Elements are
Recurring Sequences of Arbitrary Order 304--308
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 309
Mordechai Lewin Periodic Fibonacci and Lucas Sequences 310--315
G. Ferri and
M. Faccio and
A. D'Amico A New Numerical Triangle Showing Links
with Fibonacci Numbers . . . . . . . . . 316--321
Andreas N. Philippou and
Demetris L. Antzoulakos Generalized Multivariate Fibonacci
Polynomials of Order $K$ and the
Multivariate Negative Binomial
Distributions of the Same Order . . . . 322--328
Pentti Haukkanen and
Jerzy Rutkowski On Generating Functions for Powers of
Recurrence Sequences . . . . . . . . . . 329--332
Jukka Pihko A Note on a Theorem of Schinzel . . . . 333--338
Clark Kimberling Second-Order Stolarsky Arrays . . . . . 339--342
Mahesh K. Mahanthappa Arithmetic Sequences and Fibonacci
Quadratics . . . . . . . . . . . . . . . 343--346
Patricia Jones $ \phi $-Partitions . . . . . . . . . . 347--350
Clément Frappier Iterations of a Kind of Exponentials . . 351--361
Neville Robbins A New Formula for Lucas Numbers . . . . 362--363
Richard André-Jeannin Divisibility of Generalized Fibonacci
and Lucas Numbers by Their Subscripts 364--366
Robert E. Kennedy and
Curtis N. Cooper The Statistics of the Smallest Space on
a Lottery Ticket . . . . . . . . . . . . 367--370
Stanley Rabinowitz Elementary Problems and Solutions . . . 371--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Bolian Liu A Matrix Method to Solve Linear
Recurrences with Constant Coefficients 2--8
Marcellus E. Waddill The Tetranacci Sequence and
Generalizations . . . . . . . . . . . . 9--19
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 20
A. F. Horadam Negative Order Genocchi Polynomials . . 21--34
Bernard R. Hodgson On Some Number Sequences Related to the
Parity of Binomial Coefficients . . . . 35--47
Steven T. Kuhn and
Andrew Vogt Numbers Without Ones . . . . . . . . . . 48--53
Michel Deza and
Monique Laurent The Fibonacci and Parachute Inequalities
for $ l_1 $-Metrics . . . . . . . . . . 54--61
G. Ferri and
M. Faccio and
A. D'Amico Fibonacci Numbers and Ladder Network
Impedance . . . . . . . . . . . . . . . 62--67
Wai-Fong Chuan Fibonacci Words . . . . . . . . . . . . 68--76
K. Atanassov and
J. Hlebarska and
S. Mihov Recurrent Formulas of the Generalized
Fibonacci and Tribonacci Sequences . . . 77--79
Arnold Knopfmacher Elementary Properties of the Subtractive
Euclidean Algorithm . . . . . . . . . . 80--83
Anonymous Referees . . . . . . . . . . . . . . . . 84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--89
Raymond E. Whitney Advanced Problems and Solutions . . . . 90--97
Pavel Horák Strong Divisibility Linear Recurrences
of the Third Order . . . . . . . . . . . 98--101
Leonard Gillman Miscellanea . . . . . . . . . . . . . . 102
Péter Kiss and
Béla Zay On a Generalization of a Recursive
Sequence . . . . . . . . . . . . . . . . 103--109
R. B. McNeill On a Theorem of Monzingo Characterizing
the Prime Divisors of Certain Sequences
of Integers . . . . . . . . . . . . . . 110
M. W. Bunder Zeckendorf Representations Using
Negative Fibonacci Numbers . . . . . . . 111--115
Steven W. Knox Fibonacci Sequences in Finite Groups . . 116--120
D. F. Bailey More Binomial Coefficient Congruences 121--125
Anne Ludington Young $k$-Reverse Multiples . . . . . . . . . 126--131
Anonymous Announcement: Fifth International
Conference . . . . . . . . . . . . . . . 132
Richard André-Jeannin On the Equations $ U_n = U q x^2 $,
Where $q$ is Odd, and $ V_n = V q x^2 $,
Where $q$ is Even . . . . . . . . . . . 133--135
A. V. Boyd Bounds for the Catalan Numbers . . . . . 136--138
Huang Minqiang and
Dai Zongduo Projective Maps of Linear Recurring
Sequences with Maximal $p$-adic Periods 139--143
William C. Waterhouse Continued Fractions and Pythagorean
Triples . . . . . . . . . . . . . . . . 144--147
John B. Kelly Schur Functions and Fibonacci Identities 148--156
Scott Beslin and
Steve Ligh GCD-Closed Sets and the Determinants of
GCD Matrices . . . . . . . . . . . . . . 157--160
Thomas E. Moore On the Least Absolute Remainder
Euclidean Algorithm . . . . . . . . . . 161--165
Anne Ludington Young Trees for $k$-Reverse Multiples . . . . 166--174
John A. Ewell On Representations of Numbers by Sums of
Two Triangular Numbers . . . . . . . . . 175--178
Peter Griffin Acceleration of the Sum of Fibonacci
Reciprocals . . . . . . . . . . . . . . 179--181
Stanley Rabinowitz Elementary Problems and Solutions . . . 182--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
P. G. Tsangaris and
J. P. Jones And Old Theorem on the GCD and Its
Application to Primes . . . . . . . . . 194--198
Wolfdieter Lang A Combinatorial Problem in the Fibonacci
Number System and Two-Variable
Generalizations of Chebyshev's
Polynomials . . . . . . . . . . . . . . 199--210
Eliot T. Jacobson Distribution of the Fibonacci Numbers
Mod $ 2 K $ . . . . . . . . . . . . . . 211--215
Jack Y. Lee The Golden-Fibonacci Equivalence . . . . 216--220
Gordon L. Miller and
Mary T. Whalen Armstrong Numbers: $ 153 = 1^3 + 5^3 +
3^3 $ . . . . . . . . . . . . . . . . . 221--224
Piero Filipponi Waring's Formula, the Binomial Formula,
and Generalized Fibonacci Matrices . . . 225--231
Marcellus E. Waddill Some Properties of the Tetranacci
Sequence Modulo $m$ . . . . . . . . . . 232--238
A. F. Horadam Generation of Genocchi Polynomials of
First Order by Recurrence Relations . . 239--243
Yasuichi Horibe A Fibonacci Theme on Balanced Binary
Trees . . . . . . . . . . . . . . . . . 244--250
Calvin T. Long and
Shiro Ando Another Generalization of Gould's Star
of David Theorem . . . . . . . . . . . . 251--255
Ana Andrade and
S. P. Pethe On the $r$ th-Order Nonhomogeneous
Recurrence Relation and Some Generalized
Fibonacci Sequences . . . . . . . . . . 256--262
Warren Page and
K. R. S. Sastry Area-Bisecting Polygonal Paths . . . . . 263--273
Duane W. DeTemple The Triangle of Smallest Perimeter which
Circumscribes a Semicircle . . . . . . . 274
Stanley Rabinowitz Elementary Problems and Solutions . . . 275--281
Raymond E. Whitney Advanced Problems and Solutions . . . . 282--289
Allen R. Miller and
H. M. Srivastava On Glaisher's Infinite Sums Involving
the Inverse Tangent Function . . . . . . 290--294
Owen J. Brison Complete Fibonacci Sequences in Finite
Fields . . . . . . . . . . . . . . . . . 295--304
Konstantine Dabmian Zelator The Diophantine Equation $ x^2 + a^2 y^m
= z^2 n $ with $ (x, a y) = 1 $ . . . . 305--309
W. R. Spickerman and
R. N. Joyner and
R. L. Creech On the $ (2, F) $ Generalizations of the
Fibonacci Sequence . . . . . . . . . . . 310--314
Ratko To\vsi\'c and
Ivan Stojmenovi\'c Fibonacci Numbers and the Numbers of
Perfect Matchings of Square, Pentagonal,
and Hexagonal Chains . . . . . . . . . . 315--321
Earle L. Blanton, Jr. and
Spencer P. Hurd and
Judson S. McCranie On a Digraph Defined by Squaring Modulo
$n$ . . . . . . . . . . . . . . . . . . 322--333
Herta T. Freitag The Fibonacci Conference in Scotland . . 334
Edward K. Hinson On the Distribution of Pythagorean
Triples . . . . . . . . . . . . . . . . 335--338
Adina Di Porto and
Piero Filipponi Generating $M$-Strong Fibonacci
Pseudoprimes . . . . . . . . . . . . . . 339--343
Jukka Pihko On Sequences Having Same Minimal
Elements in the Lemoine--Kátai Algorithm 344--348
Frank S. Gillespie A Generalization of Kummer's Congruences
and Related Results . . . . . . . . . . 349--367
Stanley Rabinowitz Elementary Problems and Solutions . . . 368--375
Raymond E. Whitney Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
W. Moser Cyclic Binary Strings without Long Runs
of Like (Alternating) Bits . . . . . . . 2--6
I. J. Good Complex Fibonacci and Lucas Numbers,
Continued Fractions, and the Square Root
of the Golden Ratio . . . . . . . . . . 7--20
E. A. Marchisotto Connections in Mathematics: An
Introduction to Fibonacci via Pythagoras 21--27
Pentti Haukkanen Formal Power Series for Binomial Sums of
Sequences of Numbers . . . . . . . . . . 28--31
Tom C. Brown and
Peter Jau-Shyong Shiue A Remark Related to the Frobenius
Problem . . . . . . . . . . . . . . . . 32--36
Jeffrey Shallit Rational Numbers with Non-Terminating,
Non-Periodic Modified Engel-Type
Expansions . . . . . . . . . . . . . . . 37--39
Anonymous Author and Title Index for Sale . . . . 40
Vamsi K. Mootha Unary Fibonacci Numbers are
Context-Sensitive . . . . . . . . . . . 41--43
A. G. Kyriakoussis On Extended Generalized Stirling Pairs 44--51
Anonymous Book Announcement: \booktitleGeneralized
Pascal Triangles and Pyramids. Their
Fractals and Graphs and Applications, by
Boris A. Bondarenko . . . . . . . . . . 52
F. T. Howard Multinomial and $Q$-Binomial Coefficient
Modulo $4$ and Modulo $P$ . . . . . . . 53--64
W.-J. Hsu and
C. V. Page and
J.-S. Liu Fibonacci Cubes --- a Class of
Self-Similar Graphs . . . . . . . . . . 65--71
Anonymous A New Book on Liber Abaci . . . . . . . 72
Rhodes Peele and
A. J. Radcliffe and
Herbert S. Wilf Congruence Problems Involving Stirling
Numbers on the First Kind . . . . . . . 73--80
Anonymous Referees . . . . . . . . . . . . . . . . 81
Stanley Rabinowitz Elementary Problems and Solutions . . . 82--89
Raymond E. Whitney Advanced Problems and Solutions . . . . 90--97
R. Dutton and
N. Chandrasekharam and
R. Brigham On the Number of Independent Sets of
Nodes in a Tree . . . . . . . . . . . . 98--104
A. G. Shannon and
R. S. Melham Carlitz Generalizations of Lucas and
Lehmer Sequences . . . . . . . . . . . . 105--111
Ashley Melia Reiter Determining the Dimension of Fractals
Generated by Pascal's Triangle . . . . . 112--120
Paul Peart and
Leon Woodson Triple Factorization of Some Riordan
Matrices . . . . . . . . . . . . . . . . 121--128
S. Bhargava and
Chandrashekar Adiga and
D. D. Somashekara Three-Square Theorem as an Application
of Andrews' Identity . . . . . . . . . . 129--132
Anonymous Correction . . . . . . . . . . . . . . . 133
Derek Jennings Some Polynomial Identities for the
Fibonacci and Lucas Numbers . . . . . . 134--137
Anne Ludington Young A Variation on the Two-Digit Kaprekar
Routine . . . . . . . . . . . . . . . . 138--144
Anonymous Announcement: Sixth International
Conference . . . . . . . . . . . . . . . 145
Curtis Cooper and
Robert E. Kennedy On Consecutive Niven Numbers . . . . . . 146--151
Gospava B. Dordevic Mixed Fermat Convolutions . . . . . . . 152--157
Herman Haase Hyperspaces and Fibonacci Numbers . . . 158--161
Joachim Zöllner A Disjoint System of Linear Recurring
Sequences Generated by $ u_{n + 2} =
u_{n + 1} + u_n $ Which Contains Every
Natural Number . . . . . . . . . . . . . 162--164
Anonymous Book Announcement: \booktitleGeneralized
Pascal Triangles and Pyramids. Their
Fractals Graphs and Applications, by
Boris A. Bondarenko . . . . . . . . . . 165
A. F. Horadam Associated Sequences of General Order 166--172
Adino Di Porto Nonexistence of Even Fibonacci
Pseudoprimes of the 1st Kind . . . . . . 173--177
Michael J. J. Barry and
Anthony J. Lo Bello The Moment Generating Function of the
Geometric Distribution of Order $k$ . . 178--180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
Piero Filipponi and
Alwyn F. Horadam Second Derivative Sequences of Fibonacci
and Lucas Polynomials . . . . . . . . . 194--204
Dario Castellanos and
William E. Rosenthal Rational Chebyshev Approximations of
Analytic Functions . . . . . . . . . . . 205--215
Clifford S. Queen Palindromes . . . . . . . . . . . . . . 216--225
Anonymous Book Announcement: \booktitleGeneralized
Pascal Triangles and Pyramids, by Boris
A. Bondarenko . . . . . . . . . . . . . 226
C. Bender Fibonacci Transmission Lines . . . . . . 227--238
J. P. Jones and
Peter Kiss On Points Whose Coordinates Are Terms of
a Linear Recurrence . . . . . . . . . . 239--245
Scott H. Hochwald and
Jingcheng Tong On the Reciprocals of the Fibonacci
Numbers . . . . . . . . . . . . . . . . 246--250
Wai-fong Chuan Symmetric Fibonacci Words . . . . . . . 251--254
Anonymous Announcement: Sixth International
Conference . . . . . . . . . . . . . . . 255
L. C. Hsu A Summation Rule Using Stirling Numbers
of the Second Kind . . . . . . . . . . . 256--262
Michael I. Ratliff Mandelbrot's Functional Iteration and
Continued Fractions . . . . . . . . . . 263--267
François Dubeau The Rabbit Problem Revisited . . . . . . 268--273
I. J. Good Erratum for ``Complex Fibonacci and
Lucas Numbers, Continued Fractions, and
the Square Root of the Golden Ratio'' 274
John Konvalina and
Yi-Hsin Liu Circular Subsets without $q$-Separation
and Powers of Lucas Numbers . . . . . . 275
Marc S. Ordower The Connectivity of a Particular Graph 276
Stanley Rabinowitz Elementary Problems and Solutions . . . 277--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--289
Rudolph M. Najar Recursions and Pascal-Type Triangles . . 290--293
L. C. Hsu Letter to the Editor . . . . . . . . . . 294
Walter E. Beck and
Rudolph M. Najar Reduced and Augmented Amicable Pairs to
10 8 . . . . . . . . . . . . . . . . . . 295--298
Konstantine Zelator On Independent Pythagorean Numbers . . . 299--301
Pentti Haukkanen A Note on Rational Arithmetic Functions
of Order $ (2, 1) $ . . . . . . . . . . 302--306
Piero Filipponi Real Fibonacci and Lucas Numbers with
Real Subscripts . . . . . . . . . . . . 307--314
Clifford A. Reiter Fibonacci Numbers: Reduction Formulas
and Short Periods . . . . . . . . . . . 315--324
Alkiviadis G. Akritas Sylvester's Forgotten Form of the
Resultant . . . . . . . . . . . . . . . 325--332
W. R. Spickerman and
R. L. Creech and
R. N. Joyner On the Structure of the Set of the
Difference Systems Defining $ (3, F) $
Generalized Fibonacci Sequences . . . . 333--337
G. J. Rieger Sums of Unit Fractions Having Long
Continued Fractions . . . . . . . . . . 338--340
Robert E. Kennedy and
Curtis Cooper Sums of Powers of Digital Sums . . . . . 341--345
Marjorie Bicknell-Johnson Retrograde Renegades and the Pascal
Connection II: Repeating Decimals
Represented by Sequences of Diagonal
Sums of Generalized Pascal Triangles
Appearing from Right to Left . . . . . . 346--353
Gregory A. Moore A Fibonacci Polynomial Sequence Defined
by Multidimensional Continued Fractions;
and Higher-Order Golden Ratios . . . . . 354--364
Jun Wang Reduced $ \phi $-Partitions of Positive
Integers . . . . . . . . . . . . . . . . 365--369
Anonymous Announcement: Sixth International
Conference . . . . . . . . . . . . . . . 370
Stanley Rabinowitz Elementary Problems and Solutions . . . 371--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Paul Thomas Young $p$-Adic Congruences for Generalized
Fibonacci Sequences . . . . . . . . . . 2--10
Richard André-Jeannin On a Conjecture of Piero Filipponi . . . 11--13
Anonymous Announcement: Sixth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 14
Neville Robbins On Fibonacci Numbers and Primes of the
Form $ 4 k + 1 $ . . . . . . . . . . . . 15--16
Kanakku Puly Cross-Jump Numbers . . . . . . . . . . . 17
Derek Jennings On Sums of Reciprocals of Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 18--21
Gerald A. Heuer and
Ulrike Leopold-Wildburger Fibonacci-Type Sequences and Minimal
Solutions of Discrete Silverman Games 22--43
M. V. Koutras Eulerian Numbers Associated with
Sequences of Polynomials . . . . . . . . 44--57
Anonymous Referees . . . . . . . . . . . . . . . . 58--59
John M. Holte A Lucas-Type Theorem for
Fibonomial-Coefficient Residues . . . . 60--68
E. O. Hare Fibonacci Numbers and Fractional
Domination of $ P_m \times P_n $ . . . . 69--73
Amos Ehrlich Cycles in Doubling Diagrams mod $m$ . . 74--78
A. Kyriakoussis Congruences for a Wide Class of Integers
by Using Gessel's Method . . . . . . . . 79--84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Russell Jay Hendel and
Sandra A. Monteferrante Hofstadter's Extraction Conjecture . . . 98--107
M. N. Deshpande An Unexpected Encounter with the
Fibonacci Numbers . . . . . . . . . . . 108--109
Piero Filipponi and
Alwyn F. Horadam Addendum to ``Second Derivative
Sequences of Fibonacci and Lucas
Polynomials'' . . . . . . . . . . . . . 110
Diana L. Wells The Fibonacci and Lucas Triangles Modulo
2 . . . . . . . . . . . . . . . . . . . 111--123
Z. W. Trzaska Modified Numerical Triangle and the
Fibonacci Sequences . . . . . . . . . . 124--129
A. F. Horadam and
B. Swita and
P. Filipponi Integration and Derivative Sequences for
Pell and Pell--Lucas Polynomials . . . . 130--135
Robert W. Packard and
Erik S. Packard The Order of a Perfect $k$-Shuffle . . . 136--144
Charles Cassidy and
Bernard R. Hodgson On Some Properties of Fibonacci
Diagonals in Pascal's Triangle . . . . . 145--152
Paul S. Bruckman On the Infinitude of Lucas Pseudoprimes 153--154
Paul S. Bruckman Lucas Pseudoprimes are Odd . . . . . . . 155--157
Paul S. Bruckman On a Conjecture of Di Porto and
Filipponi . . . . . . . . . . . . . . . 158--159
Ed Korntved Extensions to the GCD Star of David
Theorem . . . . . . . . . . . . . . . . 160--166
J. S. Frame Fibonacci Numbers and a Chaotic
Piecewise Linear Function . . . . . . . 167--169
Pasquale J. Arpaia Generating Solutions for a Special Class
of Diophantine Equations . . . . . . . . 170--173
H. G. Grundman Sequences of Consecutive $n$-Niven
Numbers . . . . . . . . . . . . . . . . 174--175
H. W. Gould A Bracket Function Transform and Its
Inverse . . . . . . . . . . . . . . . . 176--179
Stanley Rabinowitz Elementary Problems and Solutions . . . 180--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
T. Lengyel On the Divisibility by $2$ of the
Stirling Numbers of the Second Kind . . 194--201
A. F. Horadam Unique Minimal Representation of
Integers by Negatively subscripted Pell
Numbers . . . . . . . . . . . . . . . . 202--206
Tom C. Brown Powers of Digital Sums . . . . . . . . . 207--210
Gregory A. Moore The Limit of the Golden Numbers is $ 3 /
2 $ . . . . . . . . . . . . . . . . . . 211--217
B. S. El-Desouky The Multiparameter Noncentral Stirling
Numbers . . . . . . . . . . . . . . . . 218--225
Juan Pla An ``All or None'' Divisibility Property
for a Class of Fibonacci-Like Sequences
of Integers . . . . . . . . . . . . . . 226--227
Richard André-Jeannin A Generalization of Morgan--Voyce
Polynomials . . . . . . . . . . . . . . 228--231
Ian Bruce Another Instance of the Golden Right
Triangle . . . . . . . . . . . . . . . . 232--233
Don Redmond Infinite Products and Fibonacci Numbers 234--239
A. F. Horadam Maximal Representations of Positive
Integers by Pell Numbers . . . . . . . . 240--244
Piero Filipponi and
Marco Bucci On the Integrity of Certain Fibonacci
Sums . . . . . . . . . . . . . . . . . . 245--252
W. T. Hung and
A. G. Shannon and
B. S. Thornton The Use of a Second-order Recurrence
Relation in the Diagnosis of Breast
Cancer . . . . . . . . . . . . . . . . . 253--259
Dana Carroll and
Eliot Jacobson and
Lawrence Somer Distribution of Two-Term Recurrence
Sequences Mod $ P^e $ . . . . . . . . . 260--265
W. J. A. Colman A Perfect Cuboid in Gaussian Integers 266--268
Jack Y. Lee A Note on the Negative Pascal Triangle 269--270
G. F. C. de Bruyn and
J. M. de Villiers Formulas for $ 1 + 2^p + 3^p + \cdots {}
+ n^p $ . . . . . . . . . . . . . . . . 271--276
Garry J. Tee Prime Powers of Zeros of Monic
Polynomials with Integer Coefficients 277--283
I. J. Good A Symmetry Property of Alternating Sums
of Products of Reciprocals . . . . . . . 284--287
Anonymous Announcement . . . . . . . . . . . . . . 288--289
T. V. Padmakumar A Juxtaposition Property for the $ 4
\times 4 $ Magic Square . . . . . . . . 290--292
U. Balakrishnan Some Remarks on $ \sigma (\theta (n)) $ 293--296
Wayne L. McDaniel On the Greatest Integer Function and
Lucas Sequences . . . . . . . . . . . . 297--300
Clark Kimberling The First Column of an Interspersion . . 301--315
F. T. Howard Congruences and Recurrences for
Bernoulli Numbers of Higher Orders . . . 316--328
Rama K. Govindaraju and
M. S. Krishnamoorthy and
Narsingh Deo Fibonacci Networks . . . . . . . . . . . 329--345
Wayne L. McDaniel The Irrationality of Certain Series
Whose Terms Are Reciprocals of Lucas
Sequence Terms . . . . . . . . . . . . . 346--351
George Giordano A Note on Consecutive Prime Numbers . . 352--355
Piero Filipponi and
Herta T. Freitag Fibonacci Autocorrelation Sequences . . 356--368
Pentti Haukkanen Roots of Sequences Under Covolutions . . 369--372
Stanley Rabinowitz Elementary Problems and Solutions . . . 373--378
Raymond E. Whitney Advanced Problems and Solutions . . . . 379--385
Peter Hilton and
Jean Pedersen A Note on a Geometrical Property of
Fibonacci Numbers . . . . . . . . . . . 386--388
Peter J. Grabner and
Helmut Prodinger The Fibonacci Killer . . . . . . . . . . 389--394
Michael Hauss Fibonacci, Lucas, and Central Factorial
Numbers, and $ \pi $ . . . . . . . . . . 395--396
T. Lengyel Characterizing the $2$-Adic Order of the
Logarithm . . . . . . . . . . . . . . . 397--401
Nikolai A. Volodin Number of Multinomial Coefficients not
Divisible by a Prime . . . . . . . . . . 402--406
Öystein J. Rödseth A Note on Brown and Shiue's Paper on a
Remark Related to the Frobenius Problem 407--408
A. F. Horadam An Alternative Proof of a Unique
Representation Theorem . . . . . . . . . 409--410
Anonymous New Editorial Policies . . . . . . . . . 411
Helmut Prodinger Some Information about the Binomial
Transform . . . . . . . . . . . . . . . 412--415
Jeffrey Shallit Pierce Expansions and Rules for the
Determination of Leap Years . . . . . . 416--423
R. S. Melham and
A. G. Shannon Some Congruence Properties of
Generalized Second-Order Integer
Sequences . . . . . . . . . . . . . . . 424--428
A. F. Horadam Partial Sums for Second-Order Recurrence
Sequences . . . . . . . . . . . . . . . 429--439
Anonymous Announcement . . . . . . . . . . . . . . 440
D. L. Johnson and
A. C. Kim Cyclic Fibonacci Algebras . . . . . . . 441--444
Richard André-Jeannin A Note on a General Class of Polynomials 445--454
Piero Filipponi and
Renato Menicocci and
Alwyn F. Horadam Extended Dickson Polynomials . . . . . . 455--464
Herta T. Freitag The Fibonacci Conference in Pullman . . 465--466
Stanley Rabinowitz Elementary Problems and Solutions . . . 467--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473--478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
Clark Kimberling The Zeckendorf Array Equals the Wythoff
Array . . . . . . . . . . . . . . . . . 3--8
W. R. Spickerman and
R. L. Creech and
R. N. Joyner On the $ (3, F) $ Generalizations of the
Fibonacci Sequence . . . . . . . . . . . 9--12
R. S. Melham and
A. G. Shannon Some Infinite Series Summations Using
Power Series Evaluated at a Matrix . . . 13--20
Julia Abrahams Varn Codes and Generalized Fibonacci
Trees . . . . . . . . . . . . . . . . . 21--25
Roger Webster A Combinatorial Problem with a Fibonacci
Solution . . . . . . . . . . . . . . . . 26--31
R. S. Melham and
A. G. Shannon Inverse Trigonometric Hyperbolic
Summation Formulas Involving Generalized
Fibonacci Numbers . . . . . . . . . . . 32--40
Morris Jack DeLeon Sequences Related to an Infinite Product
Expansion for the Square Root and Cube
Root Functions . . . . . . . . . . . . . 41--49
Marjorie Bicknell-Johnson and
David A. Englund Greatest Integer Identities for
Generalized Fibonacci Sequences $ \{ H_n
\} $, Where $ H_n = H_{n - 1} + H_{n -
2} $ . . . . . . . . . . . . . . . . . . 50--58
Wayne L. McDaniel Diophantine Representation of Lucas
Sequences . . . . . . . . . . . . . . . 59--63
R. S. Melham and
A. G. Shannon Some Summation Identities Using
Generalized $Q$-Matrices . . . . . . . . 64--73
Vassil S. Dimitrov and
Borislav D. Donevsky Faster Multiplication of Medium Large
Numbers Via the Zeckendorf
Representation . . . . . . . . . . . . . 74--77
Paul Thomas Young Quadratic Reciprocity Via Lucas
Sequences . . . . . . . . . . . . . . . 78--81
R. S. Melham and
A. G. Shannon A Generalization of the Catalan Identity
and Some Consequences . . . . . . . . . 82--84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
G. F. C. de Bruyn Formulas $ a + a^2 2^p + a^3 3^p +
\cdots {} + a^n n^p $ . . . . . . . . . 98--103
Wai-fong Chuan Generating Fibonacci Words . . . . . . . 104--112
Wai-fong Chuan Extraction Property of the Golden
Sequence . . . . . . . . . . . . . . . . 113--122
A. Rotkiewicz and
K. Ziemak On Even Pseudoprimes . . . . . . . . . . 123--125
R. S. Melham and
A. G. Shannon Generalizations of Some Simple
Congruences . . . . . . . . . . . . . . 126--130
P. R. Subramanian Nonzero Zeros of the Hermite Polynomials
are Irrational . . . . . . . . . . . . . 131--134
R. S. Melham and
A. G. Shannon A Generalization of a Result of D'Ocagne 135--138
Helmut Prodinger Geometric Distributions and Forbidden
Subwords . . . . . . . . . . . . . . . . 139--141
Ray Melham and
Derek Jennings On the General Linear Recurrence
Relation . . . . . . . . . . . . . . . . 142--146
N. G. Gamkrelidze On a Probabilistic Property of the
Fibonacci Sequence . . . . . . . . . . . 147--152
Arnold Knopfmacher and
M. E. Mays Pierce Expansions of Ratios and
Fibonacci and Lucas Numbers and
Polynomials . . . . . . . . . . . . . . 153--163
Peter Hope Exponential Growth of Random Fibonacci
Sequences . . . . . . . . . . . . . . . 164--168
L. C. Hsu A Difference-Operational Approach to the
Möbius Inversion Formulas . . . . . . . . 169--173
Jun Wang On the $k$ th Derivative Sequences of
Fibonacci and Lucas Polynomials . . . . 174--178
Krystyna Bialek A Note on Choudhry's Results . . . . . . 179--180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
R. S. Melham and
A. G. Shannon On Reciprocal Sums of Chebyshev Related
Sequences . . . . . . . . . . . . . . . 194--202
M. A. Khan and
Y. H. Harris Kwong Some Invariant and Minimum Properties of
Stirling Numbers of the Second Kind . . 203--205
Anatoly S. Izotov A Note on Sierpinski Numbers . . . . . . 206--207
Clark Kimberling Conjectures Concerning Irrational
Numbers and Integers . . . . . . . . . . 208--210
Peter Hilton and
Jean Pedersen and
Luc Vrancken On Certain Arithmetic Properties of
Fibonacci and Lucas Numbers . . . . . . 211--217
Roger Cook and
David Sharpe Sums of Arithmetic Progressions . . . . 218--220
Anonymous Seventh International Research
Conference . . . . . . . . . . . . . . . 221
S. D. Balkin and
D. S. Cousins and
C. K. Orr and
C. A. Reiter Short Periods of Continued Fraction
Convergents Modulo $M$: a Generalization
of the Fibonacci Case . . . . . . . . . 222--233
T. Lengyel The Order of the Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 234--239
Xiquan Shi Concerning the Recursive Sequences $
A_{n + k} = \sum_{i = 1}^k a_i
A^{a_i}_{n + i - 1} $ . . . . . . . . . 240--243
François Dubeau and
Alain Pautasso On Triangular Rectangular Numbers . . . 244--248
Krassimir T. Atanassov Remark on a New Direction for a
Generalization of the Fibonacci Sequence 249--250
Piero Filipponi Some Binomial Fibonacci Identities . . . 251--257
Lawrence Brenton and
Mi-Kyung Joo On the System of Congruences $ \Pi_{j
\not = i} n_j \equiv 1 \bmod n_i $ . . . 258--267
Alan R. Glasson Remainder Formulas Involving Generalized
Fibonacci and Lucas Polynomials . . . . 268--272
Gwang-Yeon Lee and
Sang-Gu Lee A Note on Generalized Fibonacci Numbers 273--278
Shiro Ando On a System of Sequences Defined by a
Recurrence Relation . . . . . . . . . . 279--282
Sang Geun Hahn and
Jun Kyo Kim A Note on Multiplicative Partition of
Bipartite Numbers . . . . . . . . . . . 283--289
William A. Kimball and
William A. Webb A Congruence for Fibonomial Coefficients
Modulo $ p^3 $ . . . . . . . . . . . . . 290--297
Marjorie Bicknell-Johnson and
Duane DeTemple Visualizing Golden Ratio Sums with
Tiling Patterns . . . . . . . . . . . . 298--302
Anonymous Seventh International Research
Conference . . . . . . . . . . . . . . . 303
Curtis Cooper and
Robert E. Kennedy Proof of a Result by Jarden by
Generalizing a Proof by Carlitz . . . . 304--310
Neville Robbins A Note Regarding Continued Fractions . . 311--312
Herbert Glaser and
Gerd Schöffl Ducci-Sequences and Pascal's Triangle 313--324
Piero Filipponi and
Renato Menicocci Some Probabilistic Aspects of the
Terminal Digits of Fibonacci Numbers . . 325--331
Pieter Moree and
Hans Roskam On an Arithmetical Function Related to
Euler's Totient and the Discriminator 332--340
Richard André-Jeannin A Note on a General Glass of
Polynomials, Part II . . . . . . . . . . 341--351
Tom C. Brown and
Peter Jau-shyong Shiue Squares of Second-Order Linear
Recurrence Sequences . . . . . . . . . . 352--356
Paul Bracken Dynamics of the Mapping $ f(x) = (x +
1)^{-1} $ . . . . . . . . . . . . . . . 357--358
Zhang Zhizheng and
Guo Lizhou Recurrence Sequences and Bernoulli
Polynomials of Higher Order . . . . . . 359--362
Shiro Ando and
Teluhiko Hilano A Disjoint Covering of the Set of
Natural Numbers Consisting of Sequences
Defined by a Recurrence Whose
Characteristic Equation Has a Pisot
Number Root . . . . . . . . . . . . . . 363--367
Richard Lewis Antisocial Dinner Parties . . . . . . . 368--370
Stanley Rabinowitz Elementary Problems and Solutions . . . 371--377
Raymond E. Whitney Advanced Problems and Solutions . . . . 378--385
H. W. Gould Extensions of the Hermite G.C.D.
Theorems for Binomial Coefficients . . . 386--390
Anonymous Seventh International Research
Conference . . . . . . . . . . . . . . . 391
Leetsch Charles Hsu and
Peter Jau-shyong Shiue and
Yi Wang Notes on a Conjecture of Singmaster . . 392--397
Alwyn F. Horadam and
Piero Filipponi Real Pell and Pell--Lucas Numbers with
Real Subscripts . . . . . . . . . . . . 398--406
Jovan Dj. Goli\'c On Decimation of Linear Recurring
Sequences . . . . . . . . . . . . . . . 407--411
John Konvalina Roots of Unity and Circular Subsets
without Consecutive Elements . . . . . . 412--414
K. Balasubramanian and
Roman Viveros and
N. Balakrishnan Some Discrete Distributions Related to
Extended Pascal Triangles . . . . . . . 415--425
Norbert Henze The Distribution of Spaces on Lottery
Tickets . . . . . . . . . . . . . . . . 426--431
Anne Ludington Young The Switch, Subtract, Reorder Routine 432--440
Edith H. Luchins and
Russell Hendel and
Paul Lemke and
David Tuller Linear Recurrences in Difference
Triangles . . . . . . . . . . . . . . . 441--452
Richard André-Jeannin Differential Properties of a General
Class of Polynomials . . . . . . . . . . 453--458
Odoardo Brugia and
Piero Filipponi Polynomial Divisibility in Finite
Fields, and Recurring Sequences . . . . 459--463
Juan Pla Some Conditions for ``All or None''
Divisibility of a Class of
Fibonacci-Like Sequences . . . . . . . . 464--465
Stanley Rabinowitz Elementary Problems and Solutions . . . 466--471
Raymond E. Whitney Advanced Problems and Solutions . . . . 472--477
Anonymous Volume Index . . . . . . . . . . . . . . 478
Gospava Djordjevi\'c On Some Properties of Generalized
Hermite Polynomials . . . . . . . . . . 2--6
A. F. Horadam Minmax Polynomials . . . . . . . . . . . 7--16
Anonymous Seventh International Research
Conference . . . . . . . . . . . . . . . 17
C. Elsner On the Approximation of Irrational
Numbers with Rationals Restricted by
Congruence Relations . . . . . . . . . . 18--29
E. R. Suryanarayan The Brahmagupta Polynomials . . . . . . 30--39
A. F. Horadam Jacobsthal Representation Numbers . . . 40--54
Eric Liverance and
John Pitsenberger Diagonalization of the Binomial Matrix 55--67
A. F. Horadam Extension of a Synthesis for a Class of
Polynomial Sequences . . . . . . . . . . 68--74
Richard André-Jeannin On the Existence of Even Fibonacci
Pseudoprimes with Parameters $P$ and $O$ 75--78
Anonymous Referees . . . . . . . . . . . . . . . . 79--80
Stanley Rabinowitz Elementary Problems and Solutions . . . 81--88
Raymond E. Whitney Advanced Problems and Solutions . . . . 89--97
Paul Oliverio Self-Generating Pythagorean Quadruples
and $N$-Tuples . . . . . . . . . . . . . 98--101
Michael Smith Cousins of Smith Numbers: Monica and
Suzanne Sets . . . . . . . . . . . . . . 102--104
Wayne L. McDaniel Triangular Numbers in the Pell Sequence 105--107
Bolian Liu Varol's Permutation and Its
Generalization . . . . . . . . . . . . . 108--117
Tianxin Cai On $2$-Niven Numbers and $3$-Niven
Numbers . . . . . . . . . . . . . . . . 118--120
Marjorie Bicknell-Johnson and
Colin Paul Spears Classes of Identities for the
Generalized Fibonacci Numbers $ G_n =
G_{n - 1} + G_{n - c} $ from Matrices
with Constant Valued Determinants . . . 121--128
Zdzislaw W. Trzaska On Fibonacci Hyperbolic Trigonometry and
Modified Numerical Triangles . . . . . . 129--138
Maria T. Acosta-de-Orozco and
Javier Gomez-Calderon Local Minimal Polynomials over Finite
Fields . . . . . . . . . . . . . . . . . 139--143
Tianxin Cai On $k$-Self-Numbers and Universal
Generated Numbers . . . . . . . . . . . 144--146
P. J. Grabner and
R. F. Tichy and
I. Nemes and
A. Pethö On the Least Significant Digit of
Zeckendorf Expansions . . . . . . . . . 147--151
Richard K. Guy and
William O. J. Moser Numbers of Sequences without Isolated
Odd Members . . . . . . . . . . . . . . 152--155
David C. Terr Fibonacci Expansions and ``$F$-adic
Integers'' . . . . . . . . . . . . . . . 156--163
Andrej Dujella Generalized Fibonacci Numbers and the
Problem of Diophantus . . . . . . . . . 164--174
Anonymous In Memory of Professor Steven Vajda . . 175
Gyula Darvasi and
Mihály Nagy On Repetitions in Frequency Blocks of
the Generalized Fibonacci Sequence $
u(3, 1) $ with $ u_0 = u_1 = 1 $ . . . . 176--180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
Corey Powell On the Uniqueness of Reduced
Phi-Partitions . . . . . . . . . . . . . 194--199
Edward B. Burger and
Christopher S. Kollett On the Structure of Quadratic
Irrationals Associated with Generalized
Fibonacci and Lucas Numbers . . . . . . 200--212
David Branson An Extension of Stirling Numbers . . . . 213--223
Helmut Prodinger The Asymptotic Behavior of the Golden
Numbers . . . . . . . . . . . . . . . . 224--225
Caroline Lucheta and
Eli Miller and
Clifford Reiter Digraphs from Powers Modulo $p$ . . . . 226--239
Brad Wilson Construction of Small Consecutive Niven
Numbers . . . . . . . . . . . . . . . . 240--243
F. T. Howard Sums of Powers of Integers via
Generating Functions . . . . . . . . . . 244--256
F. Dubeau and
A. G. Shannon A Fibonacci Model of Infectious Disease 257--270
Piero Filipponi On the Fibonacci Numbers Whose Subscript
is a Power . . . . . . . . . . . . . . . 271--276
Ming Luo On the Diophantine Equation $ (x (x - 1)
/ 2)^2 = (y (y - 1) / 2)^2 $ . . . . . . 277--279
Charles H. Jones Generalized Hockey Stick Identities and
$N$-Dimensional Blockwalking . . . . . . 280--289
Shen Ze Chun GCD and LCM Power Matrices . . . . . . . 290--297
Walter Carlip and
Eliot Jacobson On the Stability of Certain Lucas
Sequences Modulo $ 2^k $ . . . . . . . . 298--305
Neville Robbins Fibonacci Partitions . . . . . . . . . . 306--313
Wang Tianming and
Zhang Zhizheng Recurrence Sequences and Nörlund--Euler
Polynomials . . . . . . . . . . . . . . 314--319
Hongquan Yu and
Yi Wang and
Mingfeng He On the Limit of Generalized Golden
Numbers . . . . . . . . . . . . . . . . 320--322
J. M. H. Peters A Ten Point FFT Calculation Which
Features the Golden Ratio . . . . . . . 323--325
Pentti Haukkanen On a Binomial Sum for the Fibonacci and
Lucas Pseudoprimes . . . . . . . . . . . 326--331
Paul S. Bruckman Some Interesting Subsequences of the
Fibonacci and Lucas Pseudoprimes . . . . 332--341
A. F. Horadam Polynomials Associated with Generalized
Morgan--Voyce Polynomials . . . . . . . 342--348
David C. Terr On the Sums of Digits of Fibonacci
Numbers . . . . . . . . . . . . . . . . 349--355
E. Vantieghem On Sequences Related to Expansions of
Real Numbers . . . . . . . . . . . . . . 356--361
Valery V. Karachik $P$-Latin Matrices and Pascal's Triangle
Modulo a Prime . . . . . . . . . . . . . 362--372
Stanley Rabinowitz Elementary Problems and Solutions . . . 373--378
Raymond E. Whitney Advanced Problems and Solutions . . . . 379--385
Abdelhamid Abderrezzak Multivariate Symmetric Identities . . . 386--393
Chizhong Zhou On the $K$ th-Order Derivative Sequences
of Fibonacci and Lucas Polynomials . . . 394--408
Juan Pla On the Existence of Couples of
Second-Order Linear Recurrences with
Reciprocal Representation Properties for
Their Fibonacci Sequences . . . . . . . 409--412
Jon T. Butler and
Tsutomu Sasao Average Number of Nodes in Binary
Decision Diagrams of Fibonacci Functions 413--422
Chyi-Lung Lin On Triangular and Baker's Maps with
Golden Mean as the Parameter Value . . . 423--435
Arie Rokach Optimal Computation, by Computer, of
Fibonacci Numbers . . . . . . . . . . . 436--439
Juan Pla On the Possibility of Programming the
General $2$-by-$2$ Matrix on the Complex
Field . . . . . . . . . . . . . . . . . 440--443
H. T. Freitag and
G. M. Phillips On the Zeckendorf Form of $ F_{kn} / F_n
$ . . . . . . . . . . . . . . . . . . . 444--446
Stanley Rabinowitz Algorithmic Manipulation of Third-Order
Linear Recurrences . . . . . . . . . . . 447--464
Markus Holzer and
Peter Rossmanith A Simpler Grammar for Fibonacci Numbers 465--466
Anonymous Dedication to Herta Taussig Freitag . . 467
Stanley Rabinowitz Elementary Problems and Solutions . . . 468--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473--478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
Shiro Ando and
Masahumi Hayashi Counting the Number of Equivalence
lasses of $ (m, F) $ Sequences and Their
Generalizations . . . . . . . . . . . . 3--8
Piotr Zarzycki On Multiplicity Sequences . . . . . . . 9
Anonymous Retirement of Subscription Manager . . . 10
Piero Filipponi Modified Dickson Polynomials . . . . . . 11--18
Hongquan Yu and
Chuanguang Liang Identities Involving Partial Derivatives
of Bivariate Fibonacci and Lucas
Polynomials . . . . . . . . . . . . . . 19--23
Jürgen Spilker Initial Values for Homogeneous Linear
Recurrences of Second Order . . . . . . 24--27
Anonymous Announcement of the Eighth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 28
Jingcheng Tong The Constant for Finite Diophantine
Approximation . . . . . . . . . . . . . 29--31
Pentti Haukkanen On a Recurrence Relation in Two
Variables . . . . . . . . . . . . . . . 32--34
L. A. G. Dresel On Pseudoprimes Related to Generalized
Lucas Sequences . . . . . . . . . . . . 35--42
Peter Hilton and
Jean Pedersen and
Lawrence Somer On Lucasian Numbers . . . . . . . . . . 43--47
Peter R. Christopher and
John W. Kennedy Binomial Graphs and Their Spectra . . . 48--53
Juan Pla On Periods Modulo a Prime of Some
Classes of Sequences of Integers . . . . 54--56
Piero Filipponi An Observation of Summation Formulas for
Generalized Sequences . . . . . . . . . 57--61
Leetsch C. Hsu On a Kind Of Generalized
Arithmetic-Geometric Progression . . . . 62--67
Richard André-Jeannin Summation of Reciprocals in Certain
Second-Order Recurring Sequences . . . . 68--74
Olga Bodroza-Pantic and
Ivan Gutman and
Sven J. Cyvin Fibonacci Numbers and Algebraic
Structure Count of Some Non-Benzenoid
Conjugated Polymers . . . . . . . . . . 75--83
Herta T. Freitag A Note on the Seventh International
Conference . . . . . . . . . . . . . . . 84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Konstantine Dabmian Zelator On a Class of Non-Congruent and
Non-Pythagorean Numbers . . . . . . . . 98--101
F. Dubeau and
W. Motta and
M. Rachidi and
O. Saeki On Weighted $r$-Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 102--110
Jack Y. Lee On Some Basic Linear Properties of the
Second-Order Inhomogeneous Line-Sequence 111--121
Brad Wilson Construction of $ 2 * n $ Consecutive
$n$-Niven Numbers . . . . . . . . . . . 122--128
Chizhong Zhou A Generalization of the ``All or None''
Divisibility Property . . . . . . . . . 129--134
Helmut Prodinger On a Question of Cooper and Kennedy . . 135
Anonymous Eighth International Conference
Announcement . . . . . . . . . . . . . . 136
A. F. Horadam Jacobsthal Representation Polyomials . . 137--148
Giuseppe Ferri The Appearance of Fibonacci and Lucas
Numbers in the Simulation of Electrical
Power Lines Supplied by Two Sides . . . 149--155
Pentti Haukkanen A Note on the Bracket Function Transform 156--159
M. X. He and
D. Simon and
P. E. Ricci Dynamics of the Zeros of Fibonacci
Polynomials . . . . . . . . . . . . . . 160--168
Zhizheng Zhang Some Properties of the Generalized
Fibonacci Sequences $ C_n = C_{n - 1} +
C_{n - 2} + r $ . . . . . . . . . . . . 169--171
Jon T. Butler and
Tsutomu Sasao On the Proportion of Digits in Redundant
Numeration Systems . . . . . . . . . . . 172--180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
James Metz The Golden Staircase and the Golden Line 194--197
T. V. Padmakumar Strongly Magic Squares . . . . . . . . . 198--205
George W. Grossman Fractal Construction by Orthogonal
Projection Using the Fibonacci Sequences 206--224
Wenpeng Zhang Some Identities Involving the Fibonacci
Numbers . . . . . . . . . . . . . . . . 225--228
Harvey J. Hindin Letter to the Editor . . . . . . . . . . 229
M. N. S. Swamy On Certain Identities Involving
Fibonacci and Lucas Numbers . . . . . . 230--231
Anonymous Eighth Annual Conference Announcement 232
A. F. Horadam A Composite of Morgan--Voyce
Generalizations . . . . . . . . . . . . 233--239
Alexander Burstein and
Herbert S. Wilf On Cyclic Strings without Long Constant
Blocks . . . . . . . . . . . . . . . . . 240--247
Ray Melham Conics Which Characterize Certain Lucas
Sequences . . . . . . . . . . . . . . . 248--251
Piero Filipponi Summation Formulas for Special Lehmer
Numbers . . . . . . . . . . . . . . . . 252--257
I. Jaroszewski and
A. K. Kwa\csniewski Dynamics of the Möbius Mapping and
Fibonacci-Like Sequences . . . . . . . . 258--264
Zhizheng Zhang Some Identities Involving Generalized
Second-Order Integer Sequences . . . . . 265--267
Anonymous New Editor . . . . . . . . . . . . . . . 268
Gerd Schöffl Ducci-Processes of $4$-Tuples . . . . . 269--276
Stanley Rabinowitz Elementary Problems and Solutions . . . 277--282
Raymond E. Whitney Advanced Problems and Solutions . . . . 283--289
David Callan When Does $ m - n $ Divide $ f(m) - f(n)
$ ? A Look at Column-Finite Matrices . . 290--299
Piero Filipponi A Family of $4$-by-$4$ Fibonacci
Matrices . . . . . . . . . . . . . . . . 300--307
Anonymous New Editor and Submission of Articles 308
Julia Abrahams Couples Sequences of Generalized
Fibonacci Trees and Unequal Costs Coding
Problems . . . . . . . . . . . . . . . . 309--316
Anonymous Eighth International Conference
Announcement . . . . . . . . . . . . . . 317
W. F. Klostermeyer and
M. E. Mays and
L. Soltes and
G. Trapp A Pascal Rhombus . . . . . . . . . . . . 318--328
M. N. S. Swamy On a Class of Generalized Polynomials 329--334
Victor F. Sirvent A Semigroup Associated with the
$k$-Bonacci Numbers with Dynamic
Interpretation . . . . . . . . . . . . . 335--340
Leon C. Woodson Professor Lucas Visits the Putnam
Examination . . . . . . . . . . . . . . 341
Juan Pla The Sum of Inverses of Binomial
Coefficients Revisited . . . . . . . . . 342--345
Ezra Brown Directed Graphs Defined by Arithmetic $
\pmod {n} $ . . . . . . . . . . . . . . 346--351
A. F. Horadam and
P. Filipponi Derivative Sequences of Jacobsthal and
Jacobsthal--Lucas Polynomials . . . . . 352--357
W. R. Spickerman and
R. L. Creech The $ (2, T) $ Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 358--360
A. F. Horadam Rodriques' Formulas for Jacobsthal-Type
Polynomials . . . . . . . . . . . . . . 361--370
Stanley Rabinowitz Elementary Problems and Solutions . . . 371--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Referees . . . . . . . . . . . . . . . . 2
Michael Drmota and
Johannes Gajdosik The Parity of the Sum-of-Digits-Function
of Generalized Zeckendorf
Representations . . . . . . . . . . . . 3--19
Larry Ericksen The Pascal--De Moivre Triangles . . . . 20--33
E. R. Suryanarayan The Brahmagupta Polynomials in Two
Complex Variables . . . . . . . . . . . 34--42
James E. Voss Divisibility Tests in $N$ . . . . . . . 43--44
A. J. Reuben and
A. G. Shannon Ellipses, Cardioides, and Penrose Tiles 45--54
Anonymous Eighth International Conference
Announcement . . . . . . . . . . . . . . 55
Wayne L. McDaniel Pronic Fibonacci Numbers . . . . . . . . 56--59
Wayne L. McDaniel Pronic Lucas Numbers . . . . . . . . . . 60--62
Piero Filipponi Combinatorial Expressions for Lucas
Numbers . . . . . . . . . . . . . . . . 63--64
Albert V. Carlin A Layman's View of Music of the Spheres 65
Piero Filipponi A Note on Two Theorems of Melham and
Shannon . . . . . . . . . . . . . . . . 66--67
Zhizheng Zhang A Class of Sequences and the Aitken
Transformation . . . . . . . . . . . . . 68--71
Harald Riede Asymptotic Estimation of a Sum of Digits 72--75
Naotaka Imada A Sparse Matrix and the Catalan Numbers 76--84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Richard L. Ollerton and
Anthony G. Shannon Some Properties of Generalized Pascal
Squares and Triangles . . . . . . . . . 98--109
Gospava B. Djordjevi\'c On a Generalization of a Class of
Polynomials . . . . . . . . . . . . . . 110--117
Chyi-Lung Lin Obtaining Dividing Formulas $ n|Q(n) $
from Iterated Maps . . . . . . . . . . . 118--124
M. N. S. Swamy Brahmagupta's Theorems and Recurrence
Relations . . . . . . . . . . . . . . . 125--128
D. A. Wolfram Solving Generalized Fibonacci
Recurrences . . . . . . . . . . . . . . 129--145
Jaume Paradís and
Pelegrí Viader and
Lluís Bibiloni Approximation of Quadratic Irrationals
and Their Pierce Expansions . . . . . . 146--153
Wenpeng Zhang Some Identities Involving the Euler and
the Central Factorial Numbers . . . . . 154--157
Blair K. Spearman and
Kenneth S. Williams The Factorization of $ x^5 \pm x^3 + n $ 158--170
Clark Kimberling Palindromic Sequences from Irrational
Numbers . . . . . . . . . . . . . . . . 171--173
Richard André-Jeannin On the Integrity of Certain Infinite
Series . . . . . . . . . . . . . . . . . 174--180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
Brad Wilson The Fibonacci Triangle Modulo $p$ . . . 194--203
Nenad P. Caki\'c Note on Stirling Numbers of the Second
Kind . . . . . . . . . . . . . . . . . . 204--205
Ahmad Fawzi Alameddine Bounds on the Fibonacci Number of a
Maximal Outerplanar Graph . . . . . . . 206--210
A. Sofo and
P. Cerone On a Fibonacci Related Series . . . . . 211--215
Hüseyin Aydin and
Ramazan Dikici General Fibonacci Sequences in Finite
Groups . . . . . . . . . . . . . . . . . 216--221
John Brillhart Note on Fibonacci Primality Testing . . 222--228
Brad Wilson Power Digraphs Modulo $n$ . . . . . . . 229--239
Piero Filipponi and
Evelyn L. Hart The Zeckendorf Decomposition of Certain
Fibonacci--Lucas Products . . . . . . . 240--247
I. Tang Solving Linear Equations Using an
Optimization-Based Iterative Scheme . . 248--251
Hongquan Yu A Generalization of Stirling Numbers . . 252--258
Matú\vs Harminc and
Roman Soták Palindromic Numbers in Arithmetic
Progressions . . . . . . . . . . . . . . 259--262
Paul S. Bruckman and
Peter G. Anderson Conjectures on the $Z$-Densities of the
Fibonacci Sequence . . . . . . . . . . . 263--271
Zachary M. Franco Distribution of Binomial Coefficients
Modulo Three . . . . . . . . . . . . . . 272--275
A. Simalarides Congruences $ \bmod p^n $ for the
Bernoulli Numbers . . . . . . . . . . . 276--281
Michele Elia and
Piero Filipponi Equations of the Bring--Jerrard Form,
the Golden Section, and the Square
Fibonacci Numbers . . . . . . . . . . . 282--286
Massimo Galuzzi A Remark about the Binomial Transform 287--289
C. Elsner A Metric Result Concerning the
Approximation of Real Numbers by
Continued Fractions . . . . . . . . . . 290--294
N. Gauthier Identities for a Class of Sums Involving
Horadam's Generalized Numbers $ \{ W_n
\} $ . . . . . . . . . . . . . . . . . . 295--304
Sini\vsa Slijep\vcevi\'c A Note on Initial Digits of Recurrence
Sequences . . . . . . . . . . . . . . . 305--308
John A. Joseph A Chaotic Extension of the $ 3 x + 1 $
Function to $ Z_2 [i] $ . . . . . . . . 309--316
Neville Robbins Wilson's Theorem via Eulerian Numbers 317--318
M. A. Nyblom A Note on the Set of Almost-Isosceles
Right-Angled Triangles . . . . . . . . . 319--322
Joseph R. Siler Mean Crowds and Pythagorean Triples . . 323--326
Zhizheng Zhang and
Maixue Liu Generalizations of Some Identities
Involving Generalized Second-Order
Integer Sequences . . . . . . . . . . . 327--328
Zhizheng Zhang and
Jingyu Jin Some Identities Involving Generalized
Genocchi Polynomials and Generalized
Fibonacci--Lucas Sequences . . . . . . . 329--334
Gheorghe Udrea The Diophantine Equations $ x^2 - k =
T_n(a^2 \pm 1) $ . . . . . . . . . . . . 335--338
Xinrong Ma A Generalization of the Kummer Identity
and Its Application to Fibonacci--Lucas
Sequences . . . . . . . . . . . . . . . 339--347
I. Jaroszewski and
A. K. Kwa\csniewski Some Extensions of Properties of the
Sequence of Reciprocal Fibonacci
Polynomials . . . . . . . . . . . . . . 348--353
SeungKyung Park Complete Partitions . . . . . . . . . . 354--360
W. Carlip and
Eliot Jacobson and
Lawrence Somer Pseudoprimes, Perfect Numbers, and a
Problem of Lehmer . . . . . . . . . . . 361--371
Anonymous A Toast to Our Editor . . . . . . . . . 372
Stanley Rabinowitz Elementary Problems and Solutions . . . 373--378
Raymond E. Whitney Advanced Problems and Solutions . . . . 379--385
G. L. Cohen and
R. M. Sorli Harmonic Seeds . . . . . . . . . . . . . 386--390
A. F. Horadam Morgan--Voyce Type Generalized
Polynomials with Negative Subscripts . . 391--394
Brad Wilson Acknowledgment of Priority . . . . . . . 395
Evelyn Hart On Using Patterns in Beta-Expansions to
Study Fibonacci--Lucas Products . . . . 396--405
Anonymous New Problem Web Site . . . . . . . . . . 406
C. Cooper and
R. E. Kennedy and
M. Renberg On Certain Sums of Functions of Base $B$
Expansions . . . . . . . . . . . . . . . 407--415
Clark Kimberling Edouard Zeckendorf . . . . . . . . . . . 416--418
Anne Ludington Young Ducci-Processes of $5$-tuples . . . . . 419--433
Piotr Zarzycki Corrigendum to ``On Multiplicity
Sequences'' . . . . . . . . . . . . . . 434
F. T. Howard Lacunary Recurrences for Sums of Powers
of Integers . . . . . . . . . . . . . . 435--442
Adam M. Stinchcombe Recurrence Relations for Powers of
Recursion Sequences . . . . . . . . . . 443--447
Stefan Dantchev A Closed Form of the $ (2, F) $
Generalizations of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 448--451
Ray Melham Generalized Triple Products . . . . . . 452--456
Piero Filipponi Representing Generalized Lucas Numbers
in Terms of Their $ \alpha $-Values . . 457--462
Florian Breuer A Note on a Paper by Glaser and Schöffl 463--466
Stanley Rabinowitz Elementary Problems and Solutions . . . 467--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473
Anonymous Referees . . . . . . . . . . . . . . . . 2
M. A. Nyblom On a Generalization of the Binomial
Theorem . . . . . . . . . . . . . . . . 3--13
Lin Dazheng Fibonacci Matrices . . . . . . . . . . . 14--20
Evelyn Hart and
Laura Sanchis On the Occurrence of $ F_n $ in the
Zeckendorf Decomposition of $ n F_n $ 21--32
Anonymous Corrigendum . . . . . . . . . . . . . . 33
Mehdi Mouline and
Mustapha Rachidi Application of Markov Chains Properties
to $r$-Generalized Fibonacci Sequences 34--38
Chizhong Zhou A General Conclusion on Lucas Numbers of
the Form $ p x^2 $, Where $p$ Is Prime 39--45
Herta T. Freitag The Eighth International Conference . . 46
M. Bicknell-Johnson and
D. C. Fielder The Number of Representations of $N$
Using Distinct Fibonacci Numbers,
Counted by Recursive Formulas . . . . . 47--60
Gospava B. Dordevi\'c Polynomials Related to Morgan--Voyce
Polynomials . . . . . . . . . . . . . . 61--66
Temba Shonhiwa A Generalization of the Euler and Jordan
Totient Functions . . . . . . . . . . . 67--76
Hua-Chieh Li Fibonacci Primitive Roots and Wall's
Question . . . . . . . . . . . . . . . . 77--84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
A. Behera and
G. K. Panda On the Square Roots of Triangular
Numbers . . . . . . . . . . . . . . . . 98--105
Ray Melham Generalizations of Some Identities of
Long . . . . . . . . . . . . . . . . . . 106--110
R. S. Melham Lucas Sequences and Functions of a
$3$-by-$3$ Matrix . . . . . . . . . . . 111--115
Marjorie Bicknell-Johnson Book Review: \booktitleThe Golden Ratio
and Fibonacci Numbers, by Richard A.
Dunlap . . . . . . . . . . . . . . . . . 116
Henri Cohen On the $2$-Adic Valuations of the
Truncated Polylogarithm Series . . . . . 117--121
Stanley Rabinowitz Algorithmic Summation of Reciprocals of
Products of Fibonacci Numbers . . . . . 122--127
Herta T. Freitag and
Piero Filipponi Division of Fibonacci Numbers by $k$ . . 128--134
Henry W. Gould The Firard--Waring Power Sum Formulas
for Symmetric Functions, and Fibonacci
Sequences . . . . . . . . . . . . . . . 135--140
M. N. S. Swamy A Generalization of Jacobsthal
Polynomials . . . . . . . . . . . . . . 141--144
Anne L. Ludington-Young Even Ducci-Sequences . . . . . . . . . . 145--153
J. E. Nymann and
Ricardo A. Sáenz Eulerian Numbers: Inversion Formulas and
Congruences Modulo a Prime . . . . . . . 154--161
Stanley Rabinowitz Algorithmic Manipulation of Second-Order
Linear Recurrences . . . . . . . . . . . 162--176
Anonymous In Memoriam --- Richard Spain Vine . . . 177
Georg Johann Rieger The Golden Section and Newton
Approximation . . . . . . . . . . . . . 178--179
Stanley Rabinowitz Elementary Problems and Solutions . . . 180--184
Raymond E. Whitney Advanced Problems and Solutions . . . . 185--193
K. B. Subramaniam Almost Square Triangular Numbers . . . . 194--197
P. Viader and
J. Paradis and
Bibiloni Note on the Pierce Expansion of a
Logarithm . . . . . . . . . . . . . . . 198--202
Zhizheng Zhang Generalized Fibonacci Sequences and a
Generalization of the $Q$-Matrix . . . . 203--207
R. S. Melham Lambert Series and Elliptic Functions
and Certain Reciprocal Sums . . . . . . 208--212
M. N. Swamy Generalized Fibonacci and Lucas
Polynomials, and Their Associated
Diagonal Polynomials . . . . . . . . . . 213--222
W. Motta and
M. Rachidi and
O. Saeki On $ \infty $-Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 223--232
Temba Shonhiwa Generalized Bracket Function Inverse
Pairs . . . . . . . . . . . . . . . . . 233--239
Indulis Strazdins Partial Fibonacci and Lucas Numbers . . 240--247
R. S. Melham Sums of Certain Products of Fibonacci
and Lucas Numbers . . . . . . . . . . . 248--251
Georg J. Rieger Fibonacci Numbers and Harmonic
Quadruples . . . . . . . . . . . . . . . 252--253
Feng-Zhen Zhao Notes on Reciprocal Series Related to
Fibonacci and Lucas Numbers . . . . . . 254--257
Anatoly S. Izotov On the Form of Solutions of Martin
Davis' Diophantine Equation . . . . . . 258--261
P. Filipponi and
O. Brugia On the Integers of the Form $ n (n - 1)
- 1 $ . . . . . . . . . . . . . . . . . 262--263
Anonymous Announcement of the Ninth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 264
Florian Luca Arithmetic Functions of Fibonacci
Numbers . . . . . . . . . . . . . . . . 265--268
R. S. Melham Lucas Sequences and Functions of a
$4$-by-$4$ Matrix . . . . . . . . . . . 269--276
Stanley Rabinowitz Elementary Problems and Solutions . . . 277--281
Raymond E. Whitney Advanced Problems and Solutions . . . . 282--289
Piero Filipponi and
Michele Elia The Factorization of $ x^5 \pm p^2 x - k
$ and Fibonacci Numbers . . . . . . . . 290--298
M. A. Nyblom On Irrational Valued Series Involving
Generalized Fibonacci Numbers . . . . . 299--304
R. S. Melham Some Analogs of the Identity $ F^2_n +
F^2_{n + 1} = F_{2 n + 1} $ . . . . . . 305--311
Andrej Dujella An Extension of an Old Problem of
Diophantus and Euler . . . . . . . . . . 312--314
R. S. Melham Families of Identities Involving Sums of
Powers of the Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 315--319
A. F. Horadam Representation Grids for Certain
Morgan--Voyce Numbers . . . . . . . . . 320--325
Piero Filipponi and
Giuseppe Fierro On the Sequences $ T_n = T_{n - 1} +
T_{n - 2} + h n + k $ . . . . . . . . . 326--332
Lawrence C. Washington Some Remarks on Fibonacci Matrices . . . 333--341
Hua-Chieh Li On Second-Order Linear Recurrence
Sequences: Wall and Wyler Revisited . . 342--349
M. N. S. Swamy Network Properties of a Pair of
Generalized Polynomials . . . . . . . . 350--360
Indulis Strazdins Sieve Formulas for the Generalized
Fibonacci and Lucas Numbers . . . . . . 361--365
Anonymous Announcement of the Ninth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 366
George Woltman On the Discovery of the $ 38 $ th Known
Mersenne Prime . . . . . . . . . . . . . 367--370
Stanley Rabinowitz Elementary Problems and Solutions . . . 371--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Referees . . . . . . . . . . . . . . . . 2
R. S. Melham Sums of Certain Products of Fibonacci
and Lucas Numbers --- Part II . . . . . 3--7
M. N. S. Swamy Generalizations of Modified
Morgan--Voyce Polynomials . . . . . . . 8--16
T. MacHenry Fibonacci Fields . . . . . . . . . . . . 17--24
Carsten Elsner On Diophantine Approximations with
Rational Restricted by Arithmetical
Conditions . . . . . . . . . . . . . . . 25--34
Paul S. Bruckman On the Degree of the Characteristic
Polynomial of Powers of Sequences . . . 35--38
Neville Robbins On $t$-Core Partitions . . . . . . . . . 39--48
Florian Luca Equations Involving Arithmetic Functions
of Fibonacci and Lucas Numbers . . . . . 49--55
Leetsch Charles Hsu and
Evelyn L. Tan A Refinement of de Bruyn's Formulas for
$ \sum a^k k^p $ . . . . . . . . . . . . 56--59
Anonymous Announcement: Ninth International
Conference . . . . . . . . . . . . . . . 60
M. N. S. Swamy Rising Diagonal Polynomials Associated
with Morgan--Voyce Polynomials . . . . . 61--70
Vladimir Drobot On Primes in the Fibonacci Sequences . . 71--72
Paul Andaloro On Total Stopping Times Under $ 3 x + 1
$ Iteration . . . . . . . . . . . . . . 73--78
Tiberiu Trif Combinatorial Sums and Series Involving
Inverses of Binomial Coefficients . . . 79--83
Anonymous New Elementary Problem Editors . . . . . 84
Stanley Rabinowitz Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
J. C. Turner and
A. G. Shannon On Fibonacci Sequences, Geometry, and
the $m$-Square Equation . . . . . . . . 98--103
David A. Englund and
Marjorie Bicknell-Johnson Maximal Subscripts within Generalized
Fibonacci Sequences . . . . . . . . . . 104--113
M. N. S. Swamy Some Further Properties of André--Jeannin
and Their Companion Polynomials . . . . 114--122
R. S. Melham and
Curtis Cooper The Eigenvectors of a Certain Matrix of
Binomial Coefficients . . . . . . . . . 123--126
Julia Abrahams Nonexhaustive Generalized Fibonacci
Trees in Unequal Costs Coding Problems 127--135
Edward B. Burger and
Johathan M. Todd On Diophantine Approximation Below the
Lagrange Constant . . . . . . . . . . . 136--144
Narayanaswamy Balakrishnan and
Markos V. Koutras Random Combinations with Bounded
Differences and Cospan . . . . . . . . . 145--156
Luca Colucci and
Ottavio D'Antona and
Carlo Mereghetti Fibonacci and Lucas Numbers as
Cumulative Connection Constants . . . . 157--164
Alois Panholzer and
Helmut Prodinger Two Proofs of Filipponi's Formula for
Odd-Subscripted Lucas Numbers . . . . . 165--166
Trueman MacHenry Generalized Fibonacci and Lucas
Polynomials and Multiplicative
Arithmetic Functions . . . . . . . . . . 167--173
Sean Bradley A Geometric Connection between
Generalized Fibonacci Sequences and
Nearly Golden Sections . . . . . . . . . 174--178
Anonymous A Message of Gratitude to Stanley
Rabinowitz . . . . . . . . . . . . . . . 179
Anonymous Announcement: Ninth International
Conference . . . . . . . . . . . . . . . 180
Stanley Rabinowitz Elementary Problems and Solutions . . . 181--185
Raymond E. Whitney Advanced Problems and Solutions . . . . 186--193
Shiro Ando and
Daihachiro Sato On $p$-adic Complementary Theorems
between Pascal's Triangle and the
Modified Pascal Triangle . . . . . . . . 194--200
H. C. Williams A Number Theoretic Function Arising from
Continued Fractions . . . . . . . . . . 201--211
A. F. Horadam Uniqueness of Representations by
Morgan--Voyce Numbers . . . . . . . . . 212--215
Anonymous Announcement: Ninth International
Conference . . . . . . . . . . . . . . . 216
Bau-Sen Du Obtaining New Dividing Formulas $ n|Q(n)
$ from the Known Ones . . . . . . . . . 217--222
Zhang Wenpeng and
Yi Yuan On the Fibonacci Numbers and the
Dedekind Sums . . . . . . . . . . . . . 223--226
John M. Holte Residues of Generalized Binomial
Coefficients Modulo a Prime . . . . . . 227--238
Gospava B. Djordjevi\'c Generalized Jacobthal Polynomials . . . 239--243
Hua-Chieh Li Conditions for the Existence of
Generalized Fibonacci Primitive Roots 244--249
Marc Chamberland Families of Solutions of a Cubic
Diophantine Equation . . . . . . . . . . 250--253
R. S. Melham Alternating Sums of Fourth Powers of
Fibonacci and Lucas Numbers . . . . . . 254--259
A. F. Horadam Completion of Numerical Values of
Generalized Morgan--Voyce and Related
Polynomials . . . . . . . . . . . . . . 260--263
James H. Schmerl A Remark on Parity Sequences . . . . . . 264--271
Hua-Chieh Li Complete and Reduced Residue Systems of
Second-Order Recurrences Modulo $p$ . . 272--281
Arthur T. Benjamin and
Jennifer J. Quinn and
Francis Edward Su Phased Tilings and Generalized Fibonacci
Identities . . . . . . . . . . . . . . . 282--289
Amitabha Tripathi The Number of Solutions to $ a x + b y =
n $ . . . . . . . . . . . . . . . . . . 290--293
R. S. Melham Summation of Reciprocals which Involve
Products of Terms from Generalized
Fibonacci Sequences . . . . . . . . . . 294--298
James S. Tanton Fibonacci Numbers, Generating Sets, and
Hexagonal Properties . . . . . . . . . . 299--309
Piero Filipponi Evaluation of Certain Infinite Series
Involving Terms of Generalized Sequences 310--315
F. T. Howard In Memoriam --- Lenard Carlitz . . . . . 316
David Callan Certificates of Integrality for Linear
Binomials . . . . . . . . . . . . . . . 317--325
W. Motta and
M. Rachidi and
O. Saeki Convergent $ \infty $-Generalized
Fibonacci Sequences . . . . . . . . . . 326--333
Gospava B. Djordjevi\'c Derivative Sequences of Generalized
Jacobsthal and Jacobsthal--Lucas
Polynomials . . . . . . . . . . . . . . 334--338
I. Slavutskii A Remark on the Paper of A. Simalarides:
``Congruences Mod $p$'' for the
Bernoulli Numbers . . . . . . . . . . . 339--341
Karl Dilcher Hypergeometric Functions and Fibonacci
Numbers . . . . . . . . . . . . . . . . 342--363
Mehdi Mouline and
Mustapha Rachidi $ \infty $-Generalized Fibonacci
Sequences and Markov Chains . . . . . . 364--371
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 372--376
Raymond E. Whitney Advanced Problems and Solutions . . . . 377--385
Bouaza El Wahbi and
Mustapha Rachidi $r$-Generalized Fibonacci Sequences and
the Linear Moment Problem . . . . . . . 386--393
Margie Ribble In Memoriam --- Herta Taussig Freitag 394
Lorenz Halbeisen and
Norbert Hungerbühler Dual Form of Combinatorial Problems and
Laplace Techniques . . . . . . . . . . . 395--407
Wolfdieter Lang On Polynomials Related to Powers of the
Generating Function of Catalan's Numbers 408--419
Feng-Zhen Zhao The Integrity of Some Infinite Series 420--424
Wai-Fong Chuan and
Fei Yu Extraction Problem of the Pell Sequence 425--431
Wai-Fong Chuan and
Chih-Hao Chang and
Yen-Liang Chang Suffixes of Fibonacci Word Patterns . . 432--439
Pentti Haukkanen On the $k$-ary Convolution of
Arithmetical Functions . . . . . . . . . 440--445
R. S. Melham On an Observation of D'Ocagne Concerning
the Fundamental Sequence . . . . . . . . 446--450
A. F. Horadam Convolution Summations for Pell and
Pell--Lucas Numbers . . . . . . . . . . 451--462
Adam Stinchcombe Letter to the Editor . . . . . . . . . . 463
Omar Kihel On the Extendibility of the Set 1, 2, 5 464--466
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 467--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473--478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
George M. Phillips Report on the Ninth International
Conference . . . . . . . . . . . . . . . 3
G. L. Cohen and
R. M. Sorli Harmonic Seeds: Errata . . . . . . . . . 4
Bouazza Ell Wahbi and
Mustapha Rachidi On $r$-Generalized Fibonacci Sequences
and Hausdorff Moment Problems . . . . . 5--11
E. Munarini and
C. P. Cippo and
N. Z. Salvi On the Lucas Cubes . . . . . . . . . . . 12--21
Rajae Ben Taher and
Mustapha Rachidi Application of the $ \beta $-Algorithm
to the Ratios of $r$-Generalized
Fibonacci Sequences . . . . . . . . . . 22--26
D. Herceg and
H. Mali\vci\'c and
I. Liki\'c The Zeckendorf Numbers and the Inverses
of Some Band Matrices . . . . . . . . . 27--31
C. L. Gilbert and
J. D. Kolesar and
C. A. Reiter and
J. D. Storey Function Digraphs of Quadrative Maps
Modulo $p$ . . . . . . . . . . . . . . . 32--49
Glenn J. Fox Congruences Relating Rational Values of
Bernoulli and Euler Polynomials . . . . 50--57
M. A. Nyblom and
B. G. Sloss On the solvability of a Family of
Diophantine Equations . . . . . . . . . 58--65
Takao Komatsu On Palindromic Sequences from Irrational
Numbers . . . . . . . . . . . . . . . . 66--74
D. C. Fielder and
M. Bicknell-Johnson The First 330 Terms of Sequence A013583 75--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Abdelkrim Kihel and
Omar Kihel Sets in Which the Product of Any $K$
Elements Increased by $t$ Is a $k$ th
Power . . . . . . . . . . . . . . . . . 98--100
Steven Shattuck and
Curtis Cooper Divergent RATS Sequences . . . . . . . . 101--106
Michele Elia Derived Sequences, the Tribonacci
Recurrence and Cubic Forms . . . . . . . 107--115
Alwyn F. Horadam and
Piero Filipponi Morgan--Voyce Polynomial Derivative
Sequences . . . . . . . . . . . . . . . 116--122
Gabriela R. Sanchis and
Laura A. Sanchis On the Frequency of Occurrence of $
\alpha^i $ in the $ \alpha $-Expansions
of the Positive Integers . . . . . . . . 123--137
Gospava B. Djordjevi\'c Some Properties of Partial Derivatives
of Generalized Fibonacci and Lucas
Polynomials . . . . . . . . . . . . . . 138--141
Darrin D. Frey and
James A. Sellers Generalizing Bailey's Generalization of
the Catalan Numbers . . . . . . . . . . 142--148
M. A. Nyblom On Irrational Valued Series Involving
Generalized Fibonacci Numbers II . . . . 149--157
Gwang-Yeon Lee and
Sang-Gu Lee and
Jin-Soo Kim and
Hang-Kyun Shin The Binet Formula and Representations of
$k$-Generalized Fibonacci Numbers . . . 158--164
Fengzhen Zhao and
Tianming Wang Generalizations of Some Identities
Involving the Fibonacci Numbers . . . . 165--167
B. Bernoussi and
W. Motta and
M. Rachidi and
O. Saeki Approximation of Infinite Generalized
Fibonacci Sequences and Their Asymptotic
Binet Formula . . . . . . . . . . . . . 168--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
Jack Y. Lee Some Basic Line-Sequential Properties of
Polynomials Line-Sequences . . . . . . . 194--205
Wayne L. McDaniel On the Factorization of Lucas Numbers 206--210
Dragan Stevanovi\'c In the Number of Maximal Independent Set
of Vertices in Star-Like Ladders . . . . 211--213
Hong Hu and
Zhi-Wei Sun and
Jian-Xin Liu Reciprocal Sums of Second-Order
Recurrent Sequences . . . . . . . . . . 214--220
Jukka Pihko Remarks on the ``Greedy Odd'' Egyptian
Fraction Algorithm . . . . . . . . . . . 221--227
Zhenxiang Zhang Using Lucas Sequences to Factor Large
Integers Near Group Orders . . . . . . . 228--237
Judit Nagy Rational Points in Cantor Sets . . . . . 238--241
M. N. Deshpande and
Ezra Brown Diophantine Triplets and the Pell
Sequence . . . . . . . . . . . . . . . . 242--249
David A. Englund An Algorithm for Determining $ R(N) $
from the Subscripts of the Zeckendorf
Representation of $N$ . . . . . . . . . 250--252
H. G. Grundman An Analysis of $n$-Riven Numbers . . . . 253--255
M. A. Nyblom On the Representation of the Integers as
a Difference of Nonconsecutive
Triangular Numbers . . . . . . . . . . . 256--263
R. S. Melham Summation of Reciprocals Which Involve
Products of Terms from Generalized
Fibonacci Sequences --- Part II . . . . 264--267
Thomas M. Richardson The Filbert Matrix . . . . . . . . . . . 268--275
John A. Ewell Algorithmic Determination of the
Enumerator for Sums of Three Triangular
Numbers . . . . . . . . . . . . . . . . 276--278
Guodong Liu Identities and Congruences Involving
Higher-Order Euler--Bernoulli Numbers
and Polynomials . . . . . . . . . . . . 279--284
Harunobu Momiyama A New Recurrence Formula for Bernoulli
Numbers . . . . . . . . . . . . . . . . 285--289
Umberto Cerruti and
Gabriella Margaria Counting the Number of Solutions of
Equations in Groups by Recurrences . . . 290--298
V. Siva Rama Prasad and
B. Srinivasa Rao Pentagonal Numbers in the Associated
Pell Sequences and Diophantine Equations
$ x^2 (3 x - 1)^2 = 8 y^2 \pm 4 $ . . . 299--303
B. J. O. Franco and
Antônio Zumpano Divisibility of the Coefficients of
Chebyshev Polynomials by Primes . . . . 304--308
Dan Levy The Irreducible Factorization of
Fibonacci Polynomials Over $Q$ . . . . . 309--319
Leonard Chastkofsky The Subtractive Euclidean Algorithm and
Fibonacci Numbers . . . . . . . . . . . 320--323
Zhi-Hong Sun Invariant Sequences Under Binomial
Transformation . . . . . . . . . . . . . 324--333
Jan-Christoph Puchta The Number of $k$-Digit Fibonacci
Numbers . . . . . . . . . . . . . . . . 334--335
Takao Komatsu Continued Fractions and Newton's
Approximations, II . . . . . . . . . . . 336--338
Zhi-Hong Sun Linear Recursive Sequences and the
Powers of Matrices . . . . . . . . . . . 339--351
F. T. Howard A Tribonacci Identity . . . . . . . . . 352--357
F. T. Howard The Power of $2$ Dividing the
Coefficients of Certain Power Series . . 358--364
Clark Kimberling Symbiotic Numbers Associated with
Irrational Numbers . . . . . . . . . . . 365--372
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 373--377
Raymond E. Whitney Advanced Problems and Solutions . . . . 378--383
Anonymous Announcement of the Tenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 384--385
Mansur S. Boase A Result About the Primes Dividing
Fibonacci Numbers . . . . . . . . . . . 386--391
Fengzhen Zhao Summation of Certain Reciprocal Series
Related to the Generalized Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 392--397
Yash Puri and
Thomas Ward A Dynamical Property Unique to the Lucas
Sequence . . . . . . . . . . . . . . . . 398--402
Gospava B. Djordjevi\'c On the Generalized Laguerre Polynomials 403--407
Fengzhen Zhao and
Tianming Wang Errata for ``Generalizations of Some
Identities Involving the Fibonacci
Numbers'' . . . . . . . . . . . . . . . 408
Luis Navas Analytic Continuation of the Fibonacci
Dirichlet Series . . . . . . . . . . . . 409--418
Jack Y. Lee Some General Formulas Associated with
the Second-Order Homogeneous Polynomial
Line-Sequences . . . . . . . . . . . . . 419--429
Clark Kimberling Enumeration of Paths, Compositions of
Integers, and Fibonacci Numbers . . . . 430--435
Fengzhen Zhao and
Tianming Wang Some Identities for the Generalized
Fibonacci and Lucas Functions . . . . . 436--438
Minoru Yabuta A Simple Proof of Carmichael's Theorem
on Primitive Divisors . . . . . . . . . 439--443
Ira M. Gessel and
Tamás Lengyel On the Order of Stirling Numbers and
Alternating Binomial Coefficient Sums 444--454
Marjorie Bicknell-Johnson and
Daniel C. Fielder The Least Number Having 331
Representations as a Sum of Distinct
Fibonacci Numbers . . . . . . . . . . . 455--461
H. G. Grundman and
E. A. Teeple Generalized Happy Numbers . . . . . . . 462--466
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 467--472
Raymond E. Whitney Advanced Problems and Solutions . . . . 473--477
Anonymous Announcement of the Tenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
Wen-Jin Woan A Combinatorial Proof of a Recursive
Relation of the Motzkin Sequence by
Lattice Paths . . . . . . . . . . . . . 3--8
László Szalay On the Resolution of the Equation $ U_n
= \binom (x, 3) $ and $ V_n = \binom (x,
3) $ . . . . . . . . . . . . . . . . . . 9--12
László Tóth The Probability that $k$ Positive
Integers Are Pairwise Relatively Prime 13--18
Chu Wenchang Some Binomial Convolution Formulas . . . 19--32
Paul Thomas Young On Modified Dickson Polynomials . . . . 33--40
Wayne L. McDaniel On Fibonacci and Pell Numbers of the
Form kx 2 . . . . . . . . . . . . . . . 41--42
Paul J. Andaloro The $ 3 x + 1 $ Problem and Directed
Graphs . . . . . . . . . . . . . . . . . 43--54
Napoleon Gauthier Book Review: \booktitleFibonacci and
Lucas Numbers with Applications, by
Thomas Koshy . . . . . . . . . . . . . . 55
Neville Robbins An Alternate Proof of a Theorem of J.
Ewell . . . . . . . . . . . . . . . . . 56
Neville Robbins On the Number of Partitions into an Even
and Odd Number of Parts . . . . . . . . 57--58
Jack Y. Lee On the Morgan--Voyce Polynomial
Generalization of the First Kind . . . . 59--65
Jan-Christoph Puchta Representation of Numbers with Negative
Digits and Multiplication of Small
Integers . . . . . . . . . . . . . . . . 66--67
Jan-Christoph Puchta On the Distribution of Totients . . . . 68--70
R. S. Melham Reduction Formulas for the Summation of
Reciprocals in Certain Second-Order
Recurring Sequences . . . . . . . . . . 71--75
Florian Luca Consecutive Binomial Coefficients in
Pythagorean Triples and Squares in the
Fibonacci Sequences . . . . . . . . . . 76--78
R. B. Taher and
M. Mouline and
M. Rachidi Solving Some General Nonhomogeneous
Recurrence Relations of Order $r$ by a
Linearization Method and an Application
to Polynomial and Factorial Polynomial
Cases . . . . . . . . . . . . . . . . . 79--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--89
Anonymous Announcement of the Tenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
A. F. Horadam Morgan--Voyce Convolutions . . . . . . . 98--105
Bouazza El Wahbi and
Mehdi Mouline and
Mustapha Rachidi Solving Nonhomogeneous Recurrence
Relations of Order $r$ by Matrix Methods 106--117
Andrej Dujella An Extension of an Odd Problem of
Diophantus and Euler --- II . . . . . . 118--123
Ping-an He and
Zhizheng Zhang The Multiple Sum on the Generalized
Lucas Sequences . . . . . . . . . . . . 124--127
Ziqing Xie On the Summation of Generalized
Arithmetic-Geometric Trigonometric
Series . . . . . . . . . . . . . . . . . 128--135
Johann Leida and
Yongzhi (Peter) Yang Pascal Decompositions of Arithmetic and
Convolution Arrays in Matrices . . . . . 136--145
Rhodes Peele and
Pantelimon Stanica Matrix Powers of Column-Justified Pascal
Triangles and Fibonacci Sequences . . . 146--152
Pingzhi Yuan A Note on the Divisibility of the
Generalized Lucas Sequences . . . . . . 153--156
M. N. Deshpande and
Andrej Dujella An Interesting Property of a Recurrence
Related to the Fibonacci Sequence . . . 157--160
R. Rangarajan and
H. S. Sudheer The Brahmagupta Polynomials in Two
Complex Variables and Their Conjugates 161--169
Wenpeng Zhang and
Yuan Yi On Farey Series and Dedekind Sums . . . 170--174
Hans J. H. Tuenter Walking into an Absolute Sum . . . . . . 175--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Raymond E. Whitney Advanced Problems and Solutions . . . . 187--193
John Greene The Burgstahler Coincidence . . . . . . 194--202
Gwang-Yeon Lee and
Jin-Soo Kim and
Sang-Gu Lee Factorizations and Eigenvalues of
Fibonacci and Symmetric Fibonacci
Matrices . . . . . . . . . . . . . . . . 203--211
A. F. Horadam Convolutions for Jacobsthal-Type
Polynomials . . . . . . . . . . . . . . 212--222
A. F. Horadam Vieta Polynomials . . . . . . . . . . . 223--232
V. Siva Rama Prasad and
B. Srinivasa Rao Pentagonal Numbers in the Pell Sequence
and Diophantine Equations $ 2 x^2 = y^2
(3 y - 1)^2 \pm 2 $ . . . . . . . . . . 233--241
Anonymous Dedication to Cal Long . . . . . . . . . 242
M. A. Nyblom On the Representation of the Integers as
a Difference of Squares . . . . . . . . 243--246
Xiqiang Zhao and
Shuangshuang Dings Sequences Related to Riordan Arrays . . 247--252
James A. Sellers and
Hugh Williams On the Infinitude of Composite NSW
Numbers . . . . . . . . . . . . . . . . 253--259
Marjorie Bicknell-Johnson The Least Integer Having $p$ Fibonacci
Representations, $p$ Prime . . . . . . . 260--265
Anatoly S. Izotov Second-Order Linear Recurrences of
Composite Numbers . . . . . . . . . . . 266--268
Neville Robbins A Divisibility Property of Binary Linear
Recurrences . . . . . . . . . . . . . . 269--271
William Paulsen The Prime Number Maze . . . . . . . . . 272--279
Lin Dazheng Fibonacci--Lucas Quasi-Cyclic Matrices 280--286
Sun Ping Partition Forms of Fibonacci Numbers . . 287--289
Hong Hu On Lucas $v$-Triangles . . . . . . . . . 290--294
Arpad Benyi An Olympiad Problem, Euler's Sequence,
and Stirling's Formula . . . . . . . . . 295--298
Wolfdieter Lang On Polynomials Related to Derivatives of
the Generating Function of Catalan
Numbers . . . . . . . . . . . . . . . . 299--313
Yi Yuan and
Wenpeng Zhang Some Identities Involving the Fibonacci
Polynomials . . . . . . . . . . . . . . 314--318
B. Srinivasa Rao Heptagonal Numbers in the Lucas Sequence
and Diophantine Equations $ x^2 (5 x -
3)^2 = 20 y^2 \pm 16 $ . . . . . . . . . 319--322
W. F. Klostermeyer and
J. L. Goldwasser Nullspace-Primes and Fibonacci
Polynomials . . . . . . . . . . . . . . 323--327
Clark Kimberling Path-Counting and Fibonacci Numbers . . 328--338
Dursun Ta\csci and
Ercan Altini\csik On the Almost Hilbert--Smith Matrices 339--344
Zhi-Hong Sun Five Congruences for Primes . . . . . . 345--351
Guodong Liu Formulas for Convolution Fibonacci
Numbers and Polynomials . . . . . . . . 352--357
Pentti Haukkanen A Note on Horadam's Sequence . . . . . . 358--361
Roberto Sánchez-Peregrino Closed Formula for Poly-Bernoulli
Numbers . . . . . . . . . . . . . . . . 362--364
Neville Robbins Some Consequences of Gauss' Triangular
Number Theorem . . . . . . . . . . . . . 365--368
Patrick Costello A New Largest Smith Number . . . . . . . 369--371
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 372--378
Raymond E. Whitney Advanced Problems and Solutions . . . . 379--385
R. B. Taher and
M. Mouline and
M. Rachidi Convergence of $r$-Generalized Fibonacci
Sequences and an Extension of
Ostrowski's Condition . . . . . . . . . 386--393
Zhizheng Zhang and
Xin Wang A Note on a Class of Computational
Formulas Involving the Multiple Sum of
Recurrence Sequences . . . . . . . . . . 394--397
Anonymous The Passing of Three Fibonacci
Association Friends . . . . . . . . . . 398
Ching-Jua Chang and
Chuang-Wei Ha Eulerian Polynomials and Related
Explicit Formulas . . . . . . . . . . . 399--404
A. G. Shannon and
A. F. Horadam Reflections on the Lambda Triangle . . . 405--415
Anonymous Report on the Tenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 416
A. G. Shannon and
R. L. Ollerton Combinatorial Matrices and Linear
Recursive Sequences . . . . . . . . . . 417--423
Wenpeng Zhang On Chebyshev Polynomials and Fibonacci
Numbers . . . . . . . . . . . . . . . . 424--428
O. Krafft and
M. Schaefer On the Number of Permutations within a
Given Distance . . . . . . . . . . . . . 429--434
Lawrence Somer Generalization of a Theorem of Drobot 435--437
Jack Y. Lee On the Product of Line-Sequences . . . . 438--440
Yasuichi Horibe Fibonacci Tree Is Critically Balanced
--- a Note . . . . . . . . . . . . . . . 441--445
Giovanni Sburlati Generalized Fibonacci Sequences and
Linear Congruences . . . . . . . . . . . 446--452
F. Chaoui and
M. Mouline and
M. Rachidi Application of Markov Chains Properties
to $ \infty $-Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 453--459
Minoru Yabuta Perfect Squares in the Lucas Numbers . . 460--466
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 467--471
Raymond E. Whitney Advanced Problems and Solutions . . . . 472--478
Anonymous Volume Index . . . . . . . . . . . . . . 479
Anonymous Referees . . . . . . . . . . . . . . . . 2
Takao Komatsu The Interval Associated with a Fibonacci
Number . . . . . . . . . . . . . . . . . 3--6
Feng-Zhen Zhao and
Tianming Wang Some Identities Involving the Powers of
the Generalized Fibonacci Numbers . . . 7--12
Nathan D. Cahill and
John R. D'Errico and
John P. Spence Complex Factorizations of the Fibonacci
and Lucas Numbers . . . . . . . . . . . 13--19
K. T. Atanassov and
R. Knott and
K. Ozeki and
A. G. Shannon and
L. Szalay Inequalities among Related Pairs of
Fibonacci Numbers . . . . . . . . . . . 20--22
Xinghua Wang and
Leetsch C. Hsu A Summation Formula for Power Series
Using Eulerian Fractions . . . . . . . . 23--30
Johann Cigler $q$-Fibonacci Polynomials . . . . . . . 31--40
Paul Thomas Young On Lacunary Recurrences . . . . . . . . 41--47
Chizhong Zhou Applications of Matrix Theory to
Congruence Properties of $k$ th-Order
F-L Sequences . . . . . . . . . . . . . 48--58
R. S. Melham On Some Reciprocal Sums of Brousseau: An
Alternative Approach to That of Carlitz 59--62
J. C. Turner Some Fractals in Goldpoint Geometry . . 63--71
Tamás Lengyel Divisibility Properties by Multisection 72--79
F. T. Howard The Sum of the Squares of Two
Generalized Fibonacci Numbers . . . . . 80--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Raymond E. Whitney Advanced Problems and Solutions . . . . 91--97
Carsten Elsner On Rational Approximations by
Pythagorean Numbers . . . . . . . . . . 98--104
David Callan and
Helmut Prodinger An Involutory Matrix of Eigenvectors . . 105--107
Gwang-Yeon Lee and
Jin-Soo Kim and
Tae Ho Cho Generalized Fibonacci Functions and
Sequences of Generalized Fibonacci
Functions . . . . . . . . . . . . . . . 108--121
Florian Luca and
\vStefan Porubský The Multiplicative Group Generated by
the Lehmer Numbers . . . . . . . . . . . 122--132
Renato M. Capocelli and
Paul Cull Rounding the Solutions of Fibonacci-Like
Difference Equations . . . . . . . . . . 133--141
R. S. Melham A Fibonacci Identity in the Spirit of
Simson and Gelin--Ces\`aro . . . . . . . 142--143
Hong Feng and
Zhizheng Zhang Computational Formulas for Convoluted
Generalized Fibonacci and Lucas Numbers 144--151
M. A. Nyblom A Non-Integer Property of Elementary
Symmetric Functions in Reciprocals of
Generalized Fibonacci Numbers . . . . . 152--155
Walter Carlip and
Lawrence Somer The Existence of Special Multipliers of
Second-Order Recurrence Sequences . . . 156--168
Marjorie Bicknell-Johnson Stern's Diatomic Array Applied to
Fibonacci Representations . . . . . . . 169--179
Anonymous Tribute to JoAnn Vine . . . . . . . . . 180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
Wai-fong Chuan Characterizations of $ \alpha $-Words,
Moments, and Determinants . . . . . . . 194--208
Krystyna Grytczuk On Some Classes of Effectively
Integrable Differential Equations and
Functional Recurrences . . . . . . . . . 209--219
R. S. Melham A Three-Variable Identity Involving
Cubes of Fibonacci Numbers . . . . . . . 220--223
John A. Ewell An Elementary Proof of Jacobi's
Four-Square Theorem . . . . . . . . . . 224--228
S. Heubach and
P. Z. Chinn and
R. P. Grimaldi Rises, Levels, Drops and ``$+$'' Signs
in Compositions: Extensions of a Paper
by Alladi and Hoggatt . . . . . . . . . 229--239
A. F. Horadam Vieta Convolutions and Diagonal
Polynomials . . . . . . . . . . . . . . 240--252
Arthur Holshouser and
Harold Reiter and
James Rudzinski Dynamic One-Pile Nim . . . . . . . . . . 253--262
José Plínio O. Santos and
Milo\vs Ivkovi\'c Fibonacci Numbers and Partitions . . . . 263--278
Michele Elia and
J. Carmelo Interlando A Class of Fibonacci Ideal Lattices in $
Z[\zeta_{1 2}] $ . . . . . . . . . . . . 279--289
Belkheir Essebbar Double Indexed Fibonacci Sequences and
the Bivariate Probability Distribution 290--300
H. G. Grundman and
E. A. Teeple Heights of Happy Numbers and Cubic Happy
Numbers . . . . . . . . . . . . . . . . 301--306
Mihai Caragiu and
William Webb On Modular Fibonacci Sets . . . . . . . 307--309
Tamás Lengyel A Nim-Type Game and Continued Fractions 310--320
Pantelimon Stanica Generating Functions, Weighted and
Non-Weighted Sums for Powers of
Second-Order Recurrence Sequences . . . 321--333
Zhuo Chen and
John Greene Some Comments on Baillie--PSW
Pseudoprimes . . . . . . . . . . . . . . 334--344
Chizhong Zhou and
Fredric T. Howard On the $k$ th-Order F-L Identity . . . . 345--351
A. F. Horadam Unexpected Pell and Quasi Morgan--Voyce
Summation Connections . . . . . . . . . 352--359
Arthur T. Benjamin and
Judson D. Neer and
Daniel E. Otero and
James A. Sellers A Probabilistic View of Certain Weighted
Fibonacci Sums . . . . . . . . . . . . . 360--364
Florian Luca On Positive Numbers $n$ for Which $
\Omega (n) $ Divides $ F_n $ . . . . . . 365--371
Alan F. Beardon Sums and Differences of Values of a
Quadratic Polynomial . . . . . . . . . . 372--373
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 374--379
Florian Luca Advanced Problems and Solutions . . . . 380--383
Anonymous 11th International Conference on
Fibonacci Numbers and Their Applications 384--385
HoKyu Lee and
SeungKyung Park The $r$-Subcomplete Partitions . . . . . 386--396
Owen J. Brison and
J. Eurico Nogueira Linear Recurring Sequence Subgroups in
the Complex Field . . . . . . . . . . . 397--404
Peter Fenwick Zeckendorf Integer Arithmetic . . . . . 405--413
B. Srinivasa Rao Heptagonal Numbers in Fibonacci Sequence
and Diophantine Equations $ 4 x^2 = 5
y^2 (5 y - 3)^2 \pm 16 $ . . . . . . . . 414--420
Hung-Kuei Hsiao and
Shyr-ShenYu Mapped Shuffled Fibonacci Languages . . 421--430
Jean-Marie DeKoninck and
Nicolas Doyon On the Number of Niven Numbers up to $x$ 431--440
Ernst Herrmann Interval-Filling Sequences Involving
Reciprocal Fibonacci Numbers . . . . . . 441--449
Anonymous The Eleventh International Conference on
Fibonacci Numbers and Their Applications 450
Gwang-Yeon Lee and
Jin-Soo Kim The Linear Algebra of the Generalized
Fibonacci Matrices . . . . . . . . . . . 451--465
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 466--471
Florian Luca Advanced Problems and Solutions . . . . 472--477
Anonymous Volume Index . . . . . . . . . . . . . . 478
Anonymous Referees for 2003 . . . . . . . . . . . 2
Featured Article Fibonacci Numbers and the
Rogers--Ramanujan Identities . . . . . . 3--27
Clark Kimberling Orderings of Products of Fibonacci
Numbers . . . . . . . . . . . . . . . . 28--35
Pasquale J. Arpaia Generating Solutions for a Special Class
of Diophantine Equations II . . . . . . 36--37
Antti Karttunen On Pascal's Triangle Modulo $2$ in
Fibonacci Representation . . . . . . . . 38--46
R. S. Melham Certain Classes on Finite Sums that
Involve Generalized Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 47--54
Bernaissa Bernoussi and
Mustapha Rachidi and
Osamu Saeki Extending the Bernoulli--Euler Method
for Finding Zeros of Holomorphic
Functions . . . . . . . . . . . . . . . 55--65
Feng-Zhen Zhao and
Tianming Wang A Note on Summation of Certain
Reciprocal Series . . . . . . . . . . . 66--69
Richard P. Kubelka Self-Similarity and Symmetries of
Pascal's Triangles and Simplices . . . . 70--75
Antonio J. Di Scala and
Martín Sombra Intrinsic Palindromes . . . . . . . . . 76--81
A. F. Horadam ``Fibonacci's Liber Abaci'': A
Translation into Modern English of
Leonardo Pisano's Book of Calculation,
by L. E. Sigler . . . . . . . . . . . . 82--85
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 86--91
Florian Luca Advanced Problems and Solutions . . . . 92--97
Rajae Ben Taher and
Mustapha Rachidi On the $E$-Algorithm for Polynomial
Roots and Linear Recurrence Relations 98--105
Gospava B. Djordjevi\'c Generating Functions of the Incomplete
Generalized Fibonacci and Generalized
Lucas Numbers . . . . . . . . . . . . . 106--113
Lawrence Somer and
Walter Carlip $p$-Stability of Degenerate Second-Order
Recurrences . . . . . . . . . . . . . . 114--127
Kwang-Wu Chen Congruences for Euler Numbers . . . . . 128--140
Oleg Eterevsky and
Maxim Vsemirnov On the Number of Prime Divisors of
Higher-Order Carmichael Numbers . . . . 141--148
Wenpeng Zhang Some Identities Involving the Fibonacci
Numbers and Lucas Numbers . . . . . . . 149--154
R. S. Melham Ye Olde Fibonacci Curiosity Shoppe
Revisited . . . . . . . . . . . . . . . 155--160
R. A. Mollin and
K. Cheng Period Lengths of Continued Fractions
Involving Fibonacci Numbers . . . . . . 161--169
P. J. Rippon and
H. Taylor Even and Odd Periods in Continued
Fractions of Square Roots . . . . . . . 170--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
Xiqiang Zhao and
Shuangshuang Ding A Generalized Summation Rule Related to
Stirling Numbers . . . . . . . . . . . . 194--201
Federico Ardila The Coefficients of a Fibonacci Power
Series . . . . . . . . . . . . . . . . . 202--204
Yongzhi (Peter) Yang and
Johann Leida Pascal Decompositions of Geometric
Arrays in Matrices . . . . . . . . . . . 205--215
Nathan D. Cahill and
Darren A. Narayan Fibonacci and Lucas Numbers as
Tridiagonal Matrix Determinants . . . . 216--221
J. N. Ridley and
M. E. Mays Compositions of Unions of Graphs . . . . 222--230
Wolfdieter Lang Riccati Meets Fibonacci . . . . . . . . 231--244
Zhizheng Zhang and
Jun Wang On Some Identities Involving the
Chebyshev Polynomials . . . . . . . . . 245--249
Feng-Zhen Zhao and
Tianming Wang Some Results on Generalized Fibonacci
and Lucas Numbers and Dedekind Sums . . 250--255
Alberto Cavicchioli and
Fulvia Spaggiari Varieties of Fibonacci Type . . . . . . 256--265
David Kessler and
Jeremy Schiff A Combinatoric Proof and Generalization
of Ferguson's Formula for
$k$-Generalized Fibonacci Numbers . . . 266--273
Neville Robbins On Dedekind Sums and Linear Recurrences
of Order Two . . . . . . . . . . . . . . 274--276
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 277--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Helmut Prodinger A Note on a Paper of G. H. Weiss and M.
Dishon . . . . . . . . . . . . . . . . . 290--291
Mariano Garcia Hyperperfect Numbers with Five and Six
Different Prime Factors . . . . . . . . 292--294
Ke-Jian Wu and
Zhi-Wei Sun and
Hao Pan Some Identities for Bernoulli and Euler
Polynomials . . . . . . . . . . . . . . 295--299
Slobodan B. Tri\vckovi\'c and
Miomir S. Stankovi\'c On Periodic Solutions of a Certain
Difference Equation . . . . . . . . . . 300--305
N. Gauthier Convolving the $m$-th Powers of the
Consecutive Integers with the General
Fibonacci Sequence Using Carlitz's
Weighted Stirling Polynomials of the
Second Kind . . . . . . . . . . . . . . 306--313
Elena Barcucci and
Luc Bélanger and
Sre\vcko Brlek On Tribonacci Sequences . . . . . . . . 314--319
Benaissa Bernoussi and
Mustapha Rachidi and
Osamu Saeki Factorial Binet Formula and
Distributional Moment Formulation of
Generalized Fibonacci Sequences . . . . 320--329
Kálmán Liptai Fibonacci Balancing Numbers . . . . . . 330--340
Yi Wang and
Mingfeng He Zeros of a Class of Fibonacci-Type
Polynomials . . . . . . . . . . . . . . 341--347
Arnold Knopfmacher and
Neville Robbins On Pell Partitions . . . . . . . . . . . 348--352
M. A. Nyblom On the Construction of a Family of
Transcendental Valued Infinite Products 353--358
George M. Phillips Report on the Eleventh International
Conference on Fibonacci Numbers and
their Applications . . . . . . . . . . . 359--360
B. Bernoussi and
W. Motta and
M. Rachidi and
O. Saeki On Periodic $ \infty $-Generalized
Fibonacci Sequences . . . . . . . . . . 361--367
Neville Robbins On the Parity of the Partition Function 368--369
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 370--376
Florian Luca Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Referees . . . . . . . . . . . . . . . . 2
Paulo Ribenboim FFF: (Favorite Fibonacci Flowers) . . . 3--14
Shiro Ando and
Daihachiro Sato On GCD--LCM Duality Between Pascal's
Pyramid and the Modified Pascal Pyramid 15--21
Wai Chee Shiu and
Chuan I. Chu Distribution of the Fibonacci Numbers
Modulo $ 3^k $ . . . . . . . . . . . . . 22--28
Neville Robbins On the Infinitude of Primes of the Form
$ 3 k + 1 $ . . . . . . . . . . . . . . 29--30
Carsten Elsner On Recurrence Formulae for Sums
Involving Binomial Coefficients . . . . 31--45
Yi Wang Self-Inverse Sequences Related to a
Binomial Inverse Pair . . . . . . . . . 46--52
Neil J. Calkin and
John G. Stevens and
Diana M. Thomas A Characterization for the Length of
Cycles of the $N$-Number Ducci Game . . 53--59
Wolfgang Steiner The Joint Distribution of Greedy and
Lazy Fibonacci Expansions . . . . . . . 60--69
Yaroslav Latushkin and
Vladimir Ushakov A Representation of Regular Subsequences
of Recurrent Sequences . . . . . . . . . 70--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Florian Luca Advanced Problems and Solutions . . . . 91--97
M. A. Khan and
Harris Kwong Arithmetic Progressions with Square
Entries . . . . . . . . . . . . . . . . 98--103
Kiyota Ozeki On Weighted Fibonacci and Lucas Sums . . 104--107
A. F. Horadam Chebyshev and Pell Connections . . . . . 108--121
Jeffrey L. Meyer Symmetric Arguments in the Dedekind Sum 122--123
R. L. Ollerton and
A. G. Shannon Further Properties of Generalized
Binomial Coefficient $k$-extensions . . 124--129
Anatoly S. Izotov On the Prime Divisors of $ {\rm GCD}(3^n
- 2, 2^n - 3) $ . . . . . . . . . . . . 130--131
Guodong Liu On Congruences of Euler Numbers Modulo
an Odd Square . . . . . . . . . . . . . 132--136
Steve Fairgrieve and
Henry W. Gould Product Difference Fibonacci Identities
of Simson, Gelin--Ces\`aro, Tagiuri and
Generalizations . . . . . . . . . . . . 137--141
Neville Robbins The Lucas Triangle Revisited . . . . . . 142--148
Thomas E. Price Products of Elliptical Chord Lengths and
the Fibonacci Numbers . . . . . . . . . 149--156
Robert C. Brigham and
Julie R. Carrington and
Dal Y. Jeong and
Richard P. Vitray and
Jay Yellen Domination in Fibonacci Trees . . . . . 157--165
Mark Norfleet Characterization of Second-Order Strong
Divisibility Sequences of Polynomials 166--169
Asamoah Nkwanta and
Louis W. Shapiro Pell Walks and Riordan Matrices . . . . 170--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
B. Srinivasa Rao Heptagonal Numbers in the Pell Sequence
and Diophantine Equations $ 2 x^2 = y^2
(5 y - 3)^2 \pm 2 $ . . . . . . . . . . 194--201
Gospava B. Djordjevi\'c Some Properties of the Sequences $ C_{n,
3} = C_{n - 1, 3} + C_{n - 3, 3} + r $ 202--207
Guodong Liu and
Hui Luo Some Identities Involving Bernoulli
Numbers . . . . . . . . . . . . . . . . 208--212
Prerna Bihani and
Wendy Pusser Sheppard and
Paul Thomas Young $p$-Adic Interpolation of the Fibonacci
Sequence Via Hypergeometric Functions 213--226
Fred J. Rispoli Fibonacci Polytopes and Their
Applications . . . . . . . . . . . . . . 227--233
Emanuele Munarini Generalized $q$-Fibonacci Numbers . . . 234--242
Hei-Chi Chan The Asymptotic Growth Rate of Random
Fibonacci Type Sequences . . . . . . . . 243--255
Sergey Kitaev and
Toufik Mansour Linear Recurrences and Chebyshev
Polynomials . . . . . . . . . . . . . . 256--261
Jeffrey Shallit The Mathematics of Per Nòrgård's Rhythmic
Infinity System . . . . . . . . . . . . 262--268
Sandi Klav\vzar and
Petra \vZigert Fibonacci Cubes are the Resonance Graphs
of Fibonaccenes . . . . . . . . . . . . 269--276
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 277--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Gospava B. Djordjevi\'c On the $K$ th-order derivative sequences
of generalized Fibonacci and Lucas
polynomials . . . . . . . . . . . . . . 290--298
M. A. Nyblom On the spectrum of real numbers
revisited . . . . . . . . . . . . . . . 299--301
B. Srinivasa Rao Heptagonal numbers in the associated
Pell sequence and Diophantine equations
$ x^2 (5 x - 3)^2 = 8 y^2 \pm 4 $ . . . 302--306
Toufik Mansour Generalizations of some identities
involving the Fibonacci numbers . . . . 307--315
Michael D. Hirschhorn Non-trivial intertwined second-order
recurrence relations . . . . . . . . . . 316--325
Peter G. Anderson Book Review: \booktitleProofs that
Really Count: The Art of Combinatorial
Proof, by Arthur T. Benjamin and
Jennifer J. Quinn . . . . . . . . . . . 326--327
José Plínio O. Santos and
Milo\vs Ivkovi\'c Polynomial generalizations of the Pell
sequences and the Fibonacci sequence . . 328--338
Daniel P. Biebighauser and
Gerald A. Heuer Final digit strings of powers where the
exponents end in 1, 3, 7 or 9 . . . . . 339--350
Xia Jianguo and
Qin Hourong On reverse order numbers of certain
sequences and the Jacobi symbol . . . . 351--358
Yidong Sun Numerical triangles and several
classical sequences . . . . . . . . . . 359--370
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 371--376
Florian Luca Advanced Problems and Solutions . . . . 377--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Referees . . . . . . . . . . . . . . . . 2
Feng-Zhen Zhao and
Tianming Wang Errata for ``Some identities involving
the powers of the generalized Fibonacci
numbers'' . . . . . . . . . . . . . . . 3--6
Lawrence Somer Lucas sequences $ U_k $ for which $ U_{2
p} $ and $ U_p $ are pseudoprimes for
almost all primes $p$ . . . . . . . . . 7--12
Sean Bradley and
Patrick Brewer and
Christopher Brazfield Generalized arithmetic triangles via
convolution . . . . . . . . . . . . . . 13--19
Michael D. Hirschhorn Coupled second-order recurrences . . . . 20--25
Michael D. Hirschhorn Coupled third-order recurrences . . . . 26--31
Haixing Zhao and
Xueliang Li On the Fibonacci numbers of trees . . . 32--38
Ching-Hua Chang and
Chung-Wei Ha On identities involving Bernoulli and
Euler polynomials . . . . . . . . . . . 39--45
John M. Holte Fractal dimension of arithmetical
structures of generalized binomial
coefficients modulo a prime . . . . . . 46--58
Deidra A. Coleman and
Christopher J. Dugan and
Robert A. McEwen and
Clifford A. Reiter and
Tran T. Tang Periods of $ (q, r) $-Fibonacci
sequences and elliptic curves . . . . . 59--70
Neville Robbins On sums of three squares . . . . . . . . 71--72
Hei-Chi Chan The asymptotic growth rate of random
Fibonacci type sequences II . . . . . . 73--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Florian Luca Advanced Problems and Solutions . . . . 91--97
Jun Wang and
Xin Wang On the set of reduced $ \phi
$-partitions of a positive integer . . . 98--102
Owen J. Brison and
J. Eurico Nogueira Matrices and linear recurrences in
finite fields . . . . . . . . . . . . . 103--108
P. Bundschuh and
L. C. Hsu and
P. J.-S. Shiue Generalized Möbius inversion ---
Theoretical and computational aspects 109--116
Jiang Zeng and
Jin Zhou Applications of Waring's formula to some
identities of Chebyshev polynomials . . 117--120
Zhi-Hong Sun Primality tests for numbers of the form
$ k \cdot 2^m \pm 1 $ . . . . . . . . . 121--130
David Branson A combinatorial interpretation of
identities involving Stirling numbers
and their generalizations . . . . . . . 131--140
Hei-Chi Chan $ \pi $ in terms of $ \phi $ . . . . . . 141--144
Zhi-Hong Sun Expansions and identities concerning
Lucas sequences . . . . . . . . . . . . 145--153
Roberto B. Corcino and
Leetsch Charles Hsu and
Evelyn L. Tan A $q$-analogue of generalized Stirling
numbers . . . . . . . . . . . . . . . . 154--165
Eduardo H. M. Brietzke Generalization of an identity of Andrews 166--171
Jaroslav Seibert and
Pavel Trojovský On sums of certain products of Lucas
numbers . . . . . . . . . . . . . . . . 172--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
Douglas J. Shaw The pure numbers generated by the
Collatz sequence . . . . . . . . . . . . 194--201
John H. Jaroma On primes and terms of prime or $ 2^k $
index in the Lehmer sequences . . . . . 202--208
Christopher P. French Fifth roots of Fibonacci fractions . . . 209--215
Jovan Dj. Goli Fibonacci numbers and decimation of
binary sequences . . . . . . . . . . . . 216--223
Siguna Müller Some remarks on Williams' public-key
crypto functions . . . . . . . . . . . . 224--234
Russell Jay Hendel Linear equalities in Fibonacci numbers 235--248
Florian Luca and
Lawrence Somer Lucas sequences for which $ 4 | \phi
(|u_n|) $ for almost all $n$ . . . . . . 249--262
N. Gauthier and
Paul S. Bruckman Sums of the even integral powers of the
cosecant and secant . . . . . . . . . . 263--273
Tamás Lengyel Identities for the generating function
of the multiset $ \lfloor n \Phi^m
\rfloor $ for $ m = - 1, 1, 2 $ . . . . 274--276
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 277--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Martin W. Bunder Self matching in $ \lfloor n \alpha
\rfloor $ . . . . . . . . . . . . . . . 290--296
Joshua N. Cooper Continued fractions with partial
quotients bounded in average . . . . . . 297--301
H. W. Gould The inverse of a finite series and a
third-order recurrent sequence . . . . . 302--315
Temba Shonhiwa Compositions with pairwise relatively
prime summands within a restricted
setting . . . . . . . . . . . . . . . . 316--323
Tamás Lengyel A counting based proof of the
generalized Zeckendorf's theorem . . . . 324--325
Zhi-Hong Sun A criterion for polynomials to be
congruent to the product of linear
polynomials $ \pmod {p} $ . . . . . . . 326--329
Arthur T. Benjamin Self-avoiding walks and Fibonacci
numbers . . . . . . . . . . . . . . . . 330--334
Vedran Kr\vcadinac A new generalization of the golden ratio 335--340
C. Maniscalco Isodecimal numbers . . . . . . . . . . . 341--346
Paul Thomas Young On Lucas--Bernoulli numbers . . . . . . 347--357
Lawrence Somer Second-order linear recurrences of
composite numbers . . . . . . . . . . . 358--361
Stephan G. Wagner The Fibonacci number of generalized
Petersen graphs . . . . . . . . . . . . 362--367
Neville Robbins On the number of primitive Pythagorean
triangles with a given inradius . . . . 368--369
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 370--375
Florian Luca Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Anonymous Referees . . . . . . . . . . . . . . . . 2
Olga Bodro\vza-Panti\'c and
Angelina Ili\'c-Kova\vcevi\'c Algebraic structure count of angular
hexagonal-square chains . . . . . . . . 3--9
Lawrence Somer Special multipliers of $k$ th-order
linear recurrences modulo $ p^r $ . . . 10--21
John A. Ewell Additive evaluation of the divisor
function . . . . . . . . . . . . . . . . 22--25
C. Z. Jia and
H. M. Liu and
T. M. Wang $q$-analogs of generalized Fibonacci and
Lucas polynomials . . . . . . . . . . . 26--34
David K. Neal Fibonacci fractions from Heron's square
root approximation of the golden ratio 35--38
Arthur T. Benjamin and
Naiomi T. Cameron and
Jennifer J. Quinn Fibonacci determinants --- a
combinatorial approach . . . . . . . . . 39--55
Christian Ballot and
Michele Elia Rank and period of primes in the
Fibonacci sequence. A trichotomy . . . . 56--63
Juan B. Gil and
Michael D. Weiner and
Catalin Zara Complete Padovan sequences in finite
fields . . . . . . . . . . . . . . . . . 64--75
Wai-Fong Chuan and
Fei Yu Three new extraction formulae . . . . . 76--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Florian Luca Advanced Problems and Solutions . . . . 91--97
Florian Luca and
Laszlo Szalay Fibonacci numbers of the form $ p^a \pm
p^b + 1 $ . . . . . . . . . . . . . . . 98--103
Augustine O. Munagi Combinations with successions and
Fibonacci numbers . . . . . . . . . . . 104--114
Ron Brown and
Jonathan L. Merzel The number of Ducci sequences with given
period . . . . . . . . . . . . . . . . . 115--121
Ronald Evans and
Jonathan Pearlman Nonexistence of odd perfect numbers of a
certain form . . . . . . . . . . . . . . 122--127
Russell Jay Hendel Factorizations of $ \sum_{j = i}^{n + i
- 1} F_{a j - b} $ . . . . . . . . . . . 128--132
Guodong Liu Some computational formulas for Nörlund
numbers . . . . . . . . . . . . . . . . 133--137
Philip Matchett Wood Bijective proofs for Fibonacci
identities related to Zeckendorf's
theorem . . . . . . . . . . . . . . . . 138--145
Ming Wu and
Hao Pan Sums of products of Bernoulli numbers of
the second kind . . . . . . . . . . . . 146--150
Daniel Eloff and
Blair K. Spearman and
Kenneth S. Williams A number field with infinitely many
normal integral bases . . . . . . . . . 151--154
Greg Brockman and
Ryan J. Zerr Asymptotic behavior of certain Ducci
sequences . . . . . . . . . . . . . . . 155--163
Rong Ma and
Wenpeng Zhang Several identities involving the
Fibonacci numbers and Lucas numbers . . 164--170
Brian Curtin and
Ena Salter and
David Stone Some formulae for the Fibonacci numbers 171--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
Calvin Long and
William C. Schulz and
Shiro Ando An extension of the GCD Star of David
theorem . . . . . . . . . . . . . . . . 194--201
Thomas J. Osler Vieta-like products of nested radicals
with Fibonacci and Lucas numbers . . . . 202--204
John A. Ewell On the sum-of-divisors function . . . . 205--207
Paul S. Bruckman and
Ray S. Melham Some theorems involving powers of
generalized Fibonacci numbers at
non-equidistant points . . . . . . . . . 208--220
Hei-Chi Chan From Andrews' formula for the Fibonacci
numbers to the Rogers--Ramanujan
identities . . . . . . . . . . . . . . . 221--229
Neville Robbins A recursive formula for sums of squares 230--232
Chris Burns and
Benjamin Purcell Counting the number of winning binary
strings in the $1$-dimensional same game 233--238
Walter Carlip and
Martina Mincheva Component growth of iteration graphs
under the squaring map modulo $ p^k $ 239--246
Stephan G. Wagner The Fibonacci number of Fibonacci trees
and a related family of polynomial
recurrence systems . . . . . . . . . . . 247--253
Jens P. Bode and
Heiko Harborth and
Clark Kimberling Complementary Fibonacci sequences . . . 254--264
G. K. Panda Sequence balancing and cobalancing
numbers . . . . . . . . . . . . . . . . 265--271
Helen G. Grundman Consecutive Zeckendorf--Niven and
lazy-Fibonacci--Niven numbers . . . . . 272--276
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 277--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Anonymous In Memoriam: Patricia A. Solsaa . . . . 290
Khristo N. Boyadzhiev Derivative polynomials for $ \tanh $, $
\tan $, $ \sech $ and $ \sec $ in
explicit form . . . . . . . . . . . . . 291--303
Clark Kimberling The equation $ m^2 - 4 k = 5 n^2 $ and
unique representations of positive
integers . . . . . . . . . . . . . . . . 304--312
George M. Phillips Index-doubling in sequences by Aitken
acceleration . . . . . . . . . . . . . . 313--321
Florian Luca and
Alain Togbé On the Diophantine equation $ x^2 + 7^{2
k} = y^n $ . . . . . . . . . . . . . . . 322--326
Douglas E. Iannucci and
Florian Luca Catalan numbers, factorials, and sums of
aliquot parts . . . . . . . . . . . . . 327--336
H. W. Gould and
Jocelyn Quaintance Products of numbers which obey a
Fibonacci-type recurrence . . . . . . . 337--346
Spiros D. Dafnis and
Frosso S. Makri and
Andreas N. Philippou Restricted occupancy of $s$ kinds of
cells and generalized Pascal triangles 347--356
T. Richard Carson Periodic recurrence relations and
continued fractions . . . . . . . . . . 357--361
Minoru Yabuta The ABC-conjecture and the powerful
numbers in Lucas sequences . . . . . . . 362--365
George M. Phillips Report on the Twelfth International
Conference . . . . . . . . . . . . . . . 366--367
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 368--375
Florian Luca Advanced Problems and Solutions . . . . 376--382
Anonymous Volume Index . . . . . . . . . . . . . . 383
Joanne Catan Letter to Fibonacci Association ---
2008/2009 Subscription . . . . . . . . . 2--4
Marjorie Bicknell Johnson A Report on the Thirteenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 5--6
Arthur T. Benjamin and
Sean S. Plott A Combinatorial Approach to Fibonomial
Coefficients . . . . . . . . . . . . . . 7--9
Hayri Ardal and
David S. Gunderson and
Veselin Jungic and
Bruce M. Landman and
Kevin Williamson Ramsey Results Involving the Fibonacci
Numbers . . . . . . . . . . . . . . . . 10--17
Kenneth Edwards A Pascal-Like Triangle Related to the
Tribonacci Numbers . . . . . . . . . . . 18--25
Kyle Keepers and
Paul Thomas Young On Higher Order Lucas--Bernoulli Numbers 26--31
Hei-Chi Chan Machin-Type Formulas Expressing $ \pi $
in Terms of $ \phi $ . . . . . . . . . . 32--37
Robert Booth and
Hieu D. Nguyen Bernoulli Polynomials and Pascal's
Square . . . . . . . . . . . . . . . . . 38--47
Charles S. Kahane A Note on Ramus' Identity and Associated
Recursion Relations . . . . . . . . . . 48--52
Yufei Zhao The Coefficients of a Truncated
Fibonacci Power Series . . . . . . . . . 53--55
N. Garnier and
O. Ramaré Fibonacci Numbers and Trigonometric
Identities . . . . . . . . . . . . . . . 56--61
Thomas Stoll On Hofstadter's Married Functions . . . 62--67
Alexandru Gica Quadratic Residues in Fibonacci
Sequences . . . . . . . . . . . . . . . 68--72
Neal O. Smith On An `Uncounted' Fibonacci Identity and
Its $q$-Analogue . . . . . . . . . . . . 73--78
Neculae Vornicescu Disjoint Covering of $N$ By a
Homogeneous Linear Recurrence . . . . . 79--84
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 85--90
Florian Luca Advanced Problems and Solutions . . . . 91--97
H. G. Grundman Escalator Number Sequences . . . . . . . 98--102
Paul K. Stockmeyer A Smooth Tight Upper Bound for the
Fibonacci Representation Function $ R(n)
$ . . . . . . . . . . . . . . . . . . . 103--106
Kiyota Ozeki On Melham's Sum . . . . . . . . . . . . 107--110
Jin-Hui Fang On almost superperfect numbers . . . . . 111--114
Roger E. Zarnowski The Congruence Structure of the $ 3 x +
1 $ Map . . . . . . . . . . . . . . . . 115--125
Ligia L. Cristea and
Helmut Prodinger $q$-Enumeration of Up-Down Words By
Number of Rises . . . . . . . . . . . . 126--134
Marjorie Bicknell-Johnson Julia Robinson and Hilbert's Tenth
Problem (DVD) . . . . . . . . . . . . . 135
Guodong Liu An Identity Involving the Lucas Numbers
and Stirling Numbers . . . . . . . . . . 136--139
Pierluigi Magli Identities involving Bernoulli numbers
related to sums of powers of integers 140--145
John Greene The Unboundedness of a Family of
Difference Equations Over the Integers 146--152
Hideyuki Ohtsuka and
Shigeru Nakamura On the Sum of Reciprocal Fibonacci
Numbers . . . . . . . . . . . . . . . . 153--159
Thomas McKenzie and
Shannon Overbay Purely Periodic Second Order Linear
Recurrences . . . . . . . . . . . . . . 160--166
Mourad E. H. Ismail One Parameter Generalizations of the
Fibonacci and Lucas Numbers . . . . . . 167--180
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 181--185
Florian Luca Advanced Problems and Solutions . . . . 186--193
George Woltman and
Scott Kurowski On the discovery of the 45th and 46th
known Mersenne primes . . . . . . . . . 194--197
Lawrence Somer Lucas Pseudoprimes of Special Types . . 198--206
Helmut Prodinger On a sum of Melham and its variants . . 207--215
Florian Luca and
V. Janitzio Mejía Huguet Fibonacci--Riesel and
Fibonacci--Sierpinski numbers . . . . . 216--219
Christopher J. Hillar and
Troels Windfeldt Fibonacci Identities and Graph Colorings 220--224
Yuan He and
Qunying Liao Some Congruences Involving Euler Numbers 225--234
Szabolcs Tengely Finding $g$-gonal numbers in recurrence
sequences . . . . . . . . . . . . . . . 235--240
Dragan Ma\vsulovi\'c The Number of Finite
Homomorphism-Homogeneous Tournaments
with Loops . . . . . . . . . . . . . . . 241--244
H. W. Gould and
Jocelyn Quaintance Partial Fraction Expansions and a
Question of Bruckman . . . . . . . . . . 245--248
Dale Gerdemann Combinatorial Proofs of Zeckendorf
Family Identities . . . . . . . . . . . 249--260
Anonymous First Announcement: Fourteenth
International Conference on Fibonacci
Numbers and Their Applications . . . . . 261
Martin Griffiths Symmetric rational expressions in the
Fibonacci numbers . . . . . . . . . . . 262--267
Takao Komatsu On continued fraction expansions of
Fibonacci and Lucas Dirichlet series . . 268--278
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 279--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Ji\vrí Kla\vska On Tribonacci--Wieferich Primes . . . . 290--297
Jose M. Bonnin-Cadogan and
Christopher P. French and
Buchan Xue Continued Fractions of Roots of
Fibonacci-Like Fractions . . . . . . . . 298--311
R. S. Melham Some Conjectures Concerning Sums of Odd
Powers of Fibonacci and Lucas Numbers 312--315
Vichian Laohakosol and
Kantaphon Kuhapatanakul Reciprocal Sums of Generalized Second
Order Recurrence Sequences . . . . . . . 316--325
Khristo N. Boyadzhiev Power Sum Identities with Generalized
Stirling Numbers . . . . . . . . . . . . 326--330
Amitabha Tripathi On Pythagorean Triples Containing a
Fixed Integer . . . . . . . . . . . . . 331--340
Mohamed El Bachraoui Relatively Prime Partitions with Two and
Three Parts . . . . . . . . . . . . . . 341--345
F. Gatta and
A. D'Amico Sequences $ H_n $ for which $ H_{n + 1}
/ H_n $ Approaches the Golden Ratio . . 346--349
Trevor McGuire On the Periodicity of Certain Recursive
Sequences . . . . . . . . . . . . . . . 350--355
Marco Abrate Fibonacci Sequences of Quaternions . . . 356--365
Michael A. Nyblom On the Construction of a Family of
Almost Power Free Sequences . . . . . . 366--368
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 369--373
Florian Luca Advanced Problems and Solutions . . . . 374--380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Referees . . . . . . . . . . . . . . . . 2--3
Takashi Agoh and
Karl Dilcher Recurrence relations for Nörlund numbers
and Bernoulli numbers of the second kind 4--12
Clark Kimberling Doubly Interspersed Sequences, Double
Interspersions and Fractal Sequences . . 13--20
Ji\vrí Kla\vska and
Ladislav Skula The Cubic Character of the Tribonacci
Roots . . . . . . . . . . . . . . . . . 21--28
Emrah Kilic and
Helmut Prodinger A Generalized Filbert Matrix . . . . . . 29--33
James Mc Laughlin An Identity Motivated by an Amazing
Identity of Ramanujan . . . . . . . . . 34--38
Ismail Naci Cangul and
Musa Demirci and
Florian Luca and
Ákos Pintér and
Gökhan Soydan On the Diophantine Equation $ x^2 + 2^a
\cdot 11^b = y^n $ . . . . . . . . . . . 39--46
Chris K. Caldwell and
Takao Komatsu Some Periodicities in the Continued
Fraction Expansions of Fibonacci and
Lucas Dirichlet Series . . . . . . . . . 47--55
H. W. Gould and
Jocelyn Quaintance Generalizations of Vosmansky's Identity 56--61
Alex Eustis and
Mark Shattuck Combinatorial Proofs of Some Formulas
for $ L_m^r $ . . . . . . . . . . . . . 62--67
A. J. Macfarlane Use of Determinants to Present
Identities Involving Fibonacci and
Related Numbers . . . . . . . . . . . . 68--76
Tyler Clark and
Tom Richmond Collections of Mutually Disjoint Convex
Subsets of a Totally Ordered Set . . . . 77--79
Wenchang Chu and
Roberta R. Zhou Two Multiple Convolutions on
Fibonacci-Like Sequences . . . . . . . . 80--84
Napoleon Gauthier Thomas Koshy's \booktitleCatalan Numbers
with Applications (Book Review) . . . . 85--86
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 87--88
Florian Luca Advanced Problems and Solutions . . . . 89--97
Lawrence Somer and
Curtis Cooper Lucas $ (a_1, a_2, \ldots {}, a_k = \pm
1) $ Pseudoprimes . . . . . . . . . . . 98--113
Steve Butler and
Paul Horn and
Eric Tressler Intersecting Domino Tilings . . . . . . 114--120
Attila Bérczes and
Kálmán Liptai and
István Pink On Generalized Balancing Sequences . . . 121--128
Yan Li and
Lianrong Ma On the Elements of the Continued
Fractions of Quadratic Irrationals . . . 129--136
P.-V. Koseleff and
D. Pecker On Fibonacci Knots . . . . . . . . . . . 137--143
Amitabha Tripathi A Note on Products of Primes that Differ
by a Fixed Integer . . . . . . . . . . . 144--149
R. S. Melham On the Representation of Certain Reals
via the Golden Ratio . . . . . . . . . . 150--160
Emrah Kilic and
Eugen J. Ionascu Certain Binomial Sums with Recursive
Coefficients . . . . . . . . . . . . . . 161--167
Martin Griffiths Digit Proportions in Zeckendorf
Representations . . . . . . . . . . . . 168--174
Trevor McGuire Generalizations of the Periodicity of
Certain Recursive Sequences . . . . . . 175--181
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 182--183
Florian Luca Advanced Problems and Solutions . . . . 184--191
Anonymous Fibonacci Conference Announcement . . . 192--193
Anonymous Marjorie Bicknell-Johnson . . . . . . . 194
Charles K. Cook A Report on the Fourteenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 195--196
Nils Gaute Voll The Cassini Identity and Its Relatives 197--201
Jukka Pihko Remarks on the ``Greedy Odd'' Egyptian
Fraction Algorithm II . . . . . . . . . 202--208
Clark Kimberling Polynomials Defined by a Second-Order
Recurrence, Interlacing Zeros, and Gray
Codes . . . . . . . . . . . . . . . . . 209--218
Alan Filipin and
Bo He and
Alain Togbé On the $ D(4) $-Triple $ F_{2 k}, F_{2 k
+ 6}, F_{2 k + 4} $ . . . . . . . . . . 219--227
Ji\vrí Kla\vska and
Ladislav Skula Periods of the Tribonacci Sequence
Modulo a Prime $ p \equiv 1 \pmod {3} $ 228--235
Tatsuo Konno Sequences Constructed by a Modified
Inclusion-Exclusion Principle . . . . . 236--240
Emrah Kilic and
Ilker Akkus and
Helmut Prodinger A Proof of a Conjecture of Melham . . . 241--248
Arnold Knopfmacher and
Neville Robbins Some Properties of Cyclic Compositions 249--255
R. S. Melham On Certain Combinations of Higher Powers
of Fibonacci Numbers . . . . . . . . . . 256--259
Karl Dilcher and
Jeffrey L. Meyer Dedekind Sums and Some Generalized
Fibonacci and Lucas Sequences . . . . . 260--264
Takao Komatsu Sequences $ \{ H_n \} $ for Which $ H_{n
+ 1} / H_n $ Approaches an Irrational
Number . . . . . . . . . . . . . . . . . 265--275
Arthur T. Benjamin and
Sean S. Plott Errata --- ``Fibonacci determinants ---
a combinatorial approach'' . . . . . . . 276
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 277--282
Florian Luca Advanced Problems and Solutions . . . . 283--289
Mark Shattuck and
Tamás Waldhauser Proofs of Some Binomial Identities Using
the Method of Last Squares . . . . . . . 290--297
Charles K. Cook and
Michael R. Bacon and
Rebecca A. Hillman The ``Magicness'' of Powers of Some
Magic Squares . . . . . . . . . . . . . 298--306
R. S. Melham More on Combinations of Higher Powers of
Fibonacci Numbers . . . . . . . . . . . 307--311
Calvin Long and
Edward Korntved Extension of the GCD Star of David
Theorem to More Than Two GCDs . . . . . 312--316
Paul C. Pasles Fibonacci Matrices and Modular Forms . . 317--323
Ji\vrí Kla\vska and
Ladislav Skula A Note on the Cubic Characters of
Tribonacci Roots . . . . . . . . . . . . 324--326
Clark Kimberling Partial Sums of Generating Functions as
Polynomial Sequences . . . . . . . . . . 327--334
Thomas McKenzie and
Shannon Overbay Sums of Second Order Linear Recurrences 335--342
Cristinel Mortici Remarks on Complementary Sequences . . . 343--347
Stefano Barbero and
Umberto Cerruti and
Nadir Murru Solving the Pell Equation Via Rédei
Rational Functions . . . . . . . . . . . 348--357
Greg Back and
Mihai Caragiu The Greatest Prime Factor and Recurrent
Sequences . . . . . . . . . . . . . . . 358--362
Harris Kwong On Recurrences of Fahr and Ringel: An
Alternate Approach . . . . . . . . . . . 363--365
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 366--372
Florian Luca Advanced Problems and Solutions . . . . 373--380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Referees . . . . . . . . . . . . . . . . 2--3
Peter G. Anderson and
Marjorie Bicknell-Johnson Multidimensional Zeckendorf
Representations . . . . . . . . . . . . 4--9
G. C. Shephard Multiplicative Identities for Binomial
Coefficients . . . . . . . . . . . . . . 10--21
Miros\lawa Radziejewska and
Tomasz Schoen Additive Properties of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 22--27
Akrur Behera and
Kálmán Liptai and
Gopal Krishna Panda and
László Szalay Balancing with Fibonacci Powers . . . . 28--33
Mihai Caragiu and
Alexandru Zaharescu and
Mohammad Zaki On Ducci Sequences with Algebraic
Numbers . . . . . . . . . . . . . . . . 34--40
Russell Jay Hendel Almost-Recursiveness of Reciprocals of
Linearly Recurrent Sequences . . . . . . 41--50
Martin Griffiths Fibonacci Diagonals . . . . . . . . . . 51--56
M. A. Khan and
Harris Kwong Some Binomial Identities Associated with
the Generalized Natural Number Sequence 57--65
Christian Berg and
Antonio J. Durán Fibonacci Numbers, Euler's $2$-Periodic
Continued Fractions and Moment Sequences 66--75
Martin Griffiths Families of Fibonacci and Lucas Sums via
the Moments of a Random Variable . . . . 76--81
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 82--88
Florian Luca Advanced Problems and Solutions . . . . 89--97
Anonymous Fibonacci Conference Announcement . . . 98
Arthur T. Benjamin and
Jacob N. Scott Third and Fourth Binomial Coefficients 99--101
Jean-Marc Deshouillers and
Florian Luca On the Distribution of the Euler
Functions with Fibonacci Numbers . . . . 102--109
Michael D. Hirschhorn Factorization of Lens Sequences . . . . 110--115
Murat Kolo\uglu and
Gene S. Kopp and
Steven J. Miller and
Yinghui Wang On the Number of Summands in Zeckendorf
Decompositions . . . . . . . . . . . . . 116--130
Dhiraj Holden Results on the $ 3 x + 1 $ and $ 3 x + d
$ Conjectures . . . . . . . . . . . . . 131--133
Paul K. Romano and
Harry McLaughlin On Non-Linear Recursive Sequences and
Benford's Law . . . . . . . . . . . . . 134--138
Wenchang Chu and
Nadia N. Li Power Sums of Pell and Pell--Lucas
Polynomials . . . . . . . . . . . . . . 139--150
Vincent Russo and
Loren Schwiebert Beatty Sequences, Fibonacci Numbers, and
the Golden Ratio . . . . . . . . . . . . 151--154
Christian Avart A Characterization of Converging Ducci
Sequences Over $ Z_2 $ . . . . . . . . . 155--157
H. W. Gould and
Jocelyn Quaintance Inverting a Finite Series with Constant
Coefficients . . . . . . . . . . . . . . 158--165
Wayne L. McDaniel An Easy Determination of the Fibonacci
and Pell Squares . . . . . . . . . . . . 166--170
Jishe Feng Some New Remarks About the Dying Rabbit
Problem . . . . . . . . . . . . . . . . 171--176
Jeff Bergart A Fibonacci ``Whack'' Alongside the
Head: My Journey into the World of Book
Collecting . . . . . . . . . . . . . . . 177--179
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 180--186
Florian Luca Advanced Problems and Solutions . . . . 187--193
Anonymous Fibonacci Conference Announcement . . . 194
Clark Kimberling Beatty Sequences and Wythoff Sequences,
Generalized . . . . . . . . . . . . . . 195--200
Ralf Bundschuh and
Peter Bundschuh Distribution of Fibonacci and Lucas
Numbers Modulo $ 3^k $ . . . . . . . . . 201--210
Russell Jay Hendel Kimberling's $ \lfloor n^2 \alpha
\rfloor - n \lfloor n \alpha \rfloor $
Function . . . . . . . . . . . . . . . . 211--219
Maxim Vsemirnov Quadratic Identities For a Class of
Fibonacci-Like Polynomials . . . . . . . 220--226
Frank Ruskey Fibonacci Meets Hofstadter . . . . . . . 227--230
F. T. Howard and
Curtis Cooper Some Identities for $r$-Fibonacci
Numbers . . . . . . . . . . . . . . . . 231--242
Michael D. Hirschhorn Approximating Euler's Constant . . . . . 243--248
Martin Griffiths Fibonacci Expressions Arising From a
Coin-Tossing Scenario Involving Pairs of
Consecutive Heads . . . . . . . . . . . 249--254
Marco Abrate and
Stefano Barbero and
Umberto Cerruti and
Nadir Murru Accelerations of Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 255--266
Bassem Ghalayini and
Joseph Malkoun Golden Proportions in Higher Dimensions 267--272
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 273--280
Florian Luca Advanced Problems and Solutions . . . . 281
Arthur T. Benjamin and
Phyllis Chinn and
Jacob N. Scott and
Greg Simay Combinations of Two-Toned Tilings . . . 290
Jonas \vSiurys A Tribonacci-Like Sequence of Composite
Numbers . . . . . . . . . . . . . . . . 298
Peter G. Anderson and
Curtis Cooper Every Positive $K$-Bonacci-Like Sequence
Eventually Agrees with a Row of the
$K$-Zeckendorf Array . . . . . . . . . . 303
Ji\vrí Kla\vska and
Ladislav Skula Mordell's Equation and the Tribonacci
Family . . . . . . . . . . . . . . . . . 310
Emrah Kiliç and
Helmut Prodinger and
Ilker Akkus and
Hideyuki Ohtsuka Formulas for Fibonomial Sums with
Generalized Fibonacci and Lucas
Coefficients . . . . . . . . . . . . . . 320
Jörn Steuding What Fibonacci Numbers Have to Do with
Congruent Numbers? . . . . . . . . . . . 330
Daniel Baczkowski and
Olaolu Fasoranti and
Carrie E. Finch Lucas--Sierpi\'nski and Lucas--Riesel
Numbers . . . . . . . . . . . . . . . . 334
Min Sha On the Cycle Structure of Repeated
Exponentiation Modulo a Prime Power . . 340
Andrew V. Sills Compositions, Partitions, and Fibonacci
Numbers . . . . . . . . . . . . . . . . 348
Martin Griffiths Binet-Like Formulas From a Simple
Expansion . . . . . . . . . . . . . . . 355
Roger C. Alperin Integer Sequences Generated by $ x_{n +
1} = (x_n^2 + A) / (x_n - 1) $ . . . . . 362
Anonymous Fibonacci Conference Announcement . . . 366
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 374
Anonymous Volume Index . . . . . . . . . . . . . . 381
Jason I. Brown and
Karl Dilcher and
Dante V. Manna Series Representations of Theta
Functions in Terms of a Sequence of
Polynomials . . . . . . . . . . . . . . 5
Larry Ericksen and
Peter G. Anderson Patterns in Differences Between Rows in
$k$-Zeckendorf Arrays . . . . . . . . . 11
Joseph S. Ozbolt A New Sequence Derived From a
Combination of Cubes with Volume $ F_n^3
$ . . . . . . . . . . . . . . . . . . . 19
Wenchang Chu and
Nadia N. Li Subsequences of Fibonacci and Lucas
Polynomials with Geometric Subscripts 27
Diego Marques The Order of Appearance of Integers at
Most One Away From Fibonacci Numbers . . 36
Kantaphon Kuhapatanakul Some Connections Between a Generalized
Tribonacci Triangle and a Generalized
Fibonacci Sequence . . . . . . . . . . . 44
Brian Curtin and
Ena Salter Michael and
David Stone Lucas' Hyperbolas for Fibonacci Vectors 51
Michael A. Nyblom Sophie Germain Primes and the
Exceptional Values of the
Equal-Sum-And-Product Problem . . . . . 58
N. Gauthier Polynomial Forms for Alternating Sums of
Products of Binomial-Catalan Numbers . . 62
David Terr Some Interesting Infinite Families of
Primitive Pythagorean Triples . . . . . 68
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 82
Florian Luca Advanced Problems and Solutions . . . . 89
Anonymous Fibonacci Conference Announcement . . . 98
Nathan Hamlin and
William A. Webb Representing Positive Integers as a Sum
of Linear Recurrence Sequences . . . . . 99
Michael Behrend Proof of Kimberling's ``Even Second
Column'' Conjecture . . . . . . . . . . 106
Michael R. Bacon and
Charles K. Cook and
Russell Jay Hendel Extending Freitag's Fibonacci-Like Magic
Square to Other Dimensions . . . . . . . 119
Michael D. Hirschhorn Estimating the Apéry Numbers . . . . . . 129
Diego Marques The Order of Appearance of Product of
Consecutive Fibonacci Numbers . . . . . 132
Michael D. Hirschhorn The Number of Sequences of $n$ Tosses of
a Coin with $k$ Pairs of Consecutive
Heads . . . . . . . . . . . . . . . . . 140
Stephen R. Wassell and
Samantha Benito Edge-Length Ratios Between Dual Platonic
Solids: a Surprisingly New Result
Involving the Golden Ratio . . . . . . . 144
Diego Marques and
Pavel Trojovský On Some New Sums of Fibonomial
Coefficients . . . . . . . . . . . . . . 155
Rigoberto Flórez and
Leandro Junes GCD Properties in Hosoya's Triangle . . 163
Joshua Ide and
Marc S. Renault Power Fibonacci Sequences . . . . . . . 175
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 180
Florian Luca Advanced Problems and Solutions . . . . 187
Marjorie Bicknell Johnson A Report on the Fifteenth International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 194
Lawrence Somer and
Michal K\vrí\vzek Power Digraphs Modulo $n$ are Symmetric
of Order $M$ If and Only If $M$ is
Square Free . . . . . . . . . . . . . . 196
Sam Vandervelde On the Divisibility of Fibonacci
Sequences by Primes of Index Two . . . . 207
Marc Chamberland Finite Trigonometric Product and Sum
Identities . . . . . . . . . . . . . . . 217
Takao Komatsu Congruent Numbers and Continued
Fractions . . . . . . . . . . . . . . . 222
Kwang-Wu Chen Extensions of An Amazing Identity of
Ramanujan . . . . . . . . . . . . . . . 227
Ph. Ellia A Remark on the Radical of Odd Perfect
Numbers . . . . . . . . . . . . . . . . 231
Friedrich Pillichshammer On the Discrepancy of the Van Der Corput
Sequence Indexed by Fibonacci Numbers 235
Diego Marques The Order of Appearance of Powers of
Fibonacci and Lucas Numbers . . . . . . 239
Russell Euler and
Jawad Sadek Congruence Relations from Binet Forms 246
Marco Abrate and
Stefano Barbero and
Umberto Cerruti and
Nadir Murru Periodic Representations for Cubic
Irrationalities . . . . . . . . . . . . 252
Christian Avart Reversing Ducci Sequences . . . . . . . 265
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 272
Florian Luca Advanced Problems and Solutions . . . . 280
Marjorie Bicknell Johnson The Fibonacci Quarterly: Fifty Years . . 290
Clark Kimberling Limits of Polynomial Sequences . . . . . 294
Caroline Shapcott $C$-Color Compositions and Palindromes 297
Martin W. Bunder Horadam Functions and Powers of
Irrationals . . . . . . . . . . . . . . 304
David E. Rush Degree $n$ Relatives of the Golden Ratio
and Resultants of the Corresponding
Polynomials . . . . . . . . . . . . . . 313
Kit-Ho Mak An Analogue of the Ducci Sequences Over
Function Fields . . . . . . . . . . . . 326
A. Sofo Finite Sums in Pascal's Triangle . . . . 337
Diego Marques Fixed Points of the Order of Appearance
in the Fibonacci Sequence . . . . . . . 346
Martin Griffiths Extending the Domains of Definition of
Some Fibonacci Identities . . . . . . . 352
James Diffenderfer A Bijection Between Two Classes of
Restricted Compositions . . . . . . . . 360
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 366
Florian Luca Advanced Problems and Solutions . . . . 374
Anonymous Volume Index . . . . . . . . . . . . . . 382
Lawrence Somer and
Michal Krízek Easy Criteria to Determine if a Prime
Divides Certain Second-Order Recurrences 3
Olivia Beckwith and
Amanda Bower and
Louis Gaudet and
Rachel Insoft and
Shiyu Li and
Steven J. Miller and
Philip Tosteson The Average Gap Distribution For
Generalized Zeckendorf Decompositions 13
Ovidiu D. Bagdasar and
Peter J. Larcombe On the Characterization of Periodic
Complex Horadam Sequences . . . . . . . 28
Diego Marques The Order of Appearance of the Product
of Consecutive Lucas Numbers . . . . . . 38
Constantinos Georghiou and
Andreas N. Philippou and
Abolfazl Saghafi On the Modes of the Poisson Distribution
of Order $k$ . . . . . . . . . . . . . . 44
Kantaphon Kuhapatanakul and
Rattanapol Wasutharat Expressions for the Products of the
Second Order Linear Recurrences . . . . 49
Joseph B. Dence and
Thomas P. Dence On Inverse Relations for General Lucas
Sequences of Polynomials . . . . . . . . 55
Mark Shattuck Combinatorial Proofs of Determinant
Formulas for the Fibonacci and Lucas
Polynomials . . . . . . . . . . . . . . 63
A. Schinzel On Divisibility by $ (a^k - b^k) / (a -
b) $ . . . . . . . . . . . . . . . . . . 72
Diego Marques and
James A. Sellers and
Pavel Trojovský On Divisibility Properties of Certain
Fibonomial Coefficients by a Prime . . . 78
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 84
Florian Luca Advanced Problems and Solutions . . . . 91
John B. Cosgrave and
Karl Dilcher Pairs of Reciprocal Quadratic
Congruences Involving Primes . . . . . . 98
Florian Luca and
Aynur Yalçiner $L$-Functions of Elliptic Curves and
Fibonacci Numbers . . . . . . . . . . . 112
A. Schinzel A Property of Lehmer Numbers . . . . . . 119
Michael D. Hirschhorn and
Vasile Sinescu Elementary Algebra in Ramanujan's Lost
Notebook . . . . . . . . . . . . . . . . 123
Alexander Collins and
Charles Dedrickson and
Hua Wang Binary Words, $n$-Color Compositions and
Bisection of the Fibonacci Numbers . . . 130
Christian Avart A Result About Cycles in Ducci Sequences 137
Romeo Me\vstrovi\'c A Lucas Type Theorem Modulo Prime Powers 142
John Estes and
William Staton and
Bing Wei Independent Sets of Cardinality $s$ of
Maximal Outerplanar Graphs . . . . . . . 147
Brandon Avila and
Yongyi Chen On Moduli For Which the Lucas Numbers
Contain a Complete Residue System . . . 151
Emrah Kílíç and
Helmut Prodinger Variants of the Filbert Matrix . . . . . 153
Michael D. Hirschhorn The Asymptotic Behavior of $ \prod_{k =
0}^n n \choose k $ . . . . . . . . . . . 163
Peter J. Larcombe and
Ovidiu D. Bagdasar On a Result of Bunder Involving Horadam
Sequences: a Proof and Generalization 174
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 177
Florian Luca Advanced Problems and Solutions . . . . 186
Lawrence Somer and
Michal Krízek Prime Lehmer and Lucas Numbers With
Composite Indices . . . . . . . . . . . 194
Michael D. Hirschhorn Estimating the Apéry Numbers II . . . . . 215
Jonny Griffiths and
Martin Griffiths Fibonacci-Related Sequences via Iterated
QRT Maps . . . . . . . . . . . . . . . . 218
Florian Luca and
Laszlo Szalay On the Counting Function of Triples
Whose Pairwise Products Are Close to
Fibonacci Numbers . . . . . . . . . . . 228
Diego Marques Sharper Upper Bounds for the Order of
Appearance in the Fibonacci Sequence . . 233
G. K. Panda and
S. S. Rout Gap Balancing Numbers . . . . . . . . . 239
Connor Ahlbach and
Jeremy Usatine and
Christiane Frougny and
Nicholas Pippenger Efficient Algorithms for Zeckendorf
Arithmetic . . . . . . . . . . . . . . . 249
Michael D. Hirschhorn A Naive Proof that $ F_{5n} \equiv 0
\pmod 5 $ . . . . . . . . . . . . . . . 256
Daryl Deford Counting Rearrangements on Generalized
Wheel Graphs . . . . . . . . . . . . . . 259
Nils Gaute Voll Some Identities for Four Term Recurrence
Relations . . . . . . . . . . . . . . . 268
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 274
Florian Luca Advanced Problems and Solutions . . . . 282
Anonymous Fibonacci Conference Announcement . . . 288
Lawrence Somer and
Michal K\vrí\vzek Fixed Points and Upper Bounds for the
Rank of Appearance in Lucas Sequences 291
Chatchawan Panraksa and
Aram Tangboonduangjit and
Keng Wiboonton Exact Divisibility Properties of Some
Subsequences of Fibonacci Numbers . . . 307
Christian Ballot On Zeckendorf and Base $b$ Digit Sums 319
Michael D. Hirschhorn The Number of $1$'s in the Partitions of
$n$ . . . . . . . . . . . . . . . . . . 326
Cheng Lien Lang and
Mong Lung Lang Fibonacci Numbers and Identities . . . . 330
Ovidiu D. Bagdasar and
Peter J. Larcombe On the Number of Complex Horadam
Sequences with a Fixed Period . . . . . 339
Christian Richter A Note on Perfect Tilings of Rectangles
with Rectangles . . . . . . . . . . . . 348
Leonid Bedratyuk Derivations and Identitites for
Fibonacci and Lucas Polynomials . . . . 351
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 374
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Fibonacci Conference Announcement . . . 2
Mohamed Taoufiq Damir and
Bernadette Faye and
Florian Luca and
Amadou Tall Members of Lucas Sequences Whose Euler
Function Is a Power of $2$ . . . . . . . 3
Michael D. Hirschhorn The Number of Different Parts in the
Partitions of $n$ . . . . . . . . . . . 10
Neville Robbins On Tribonacci Numbers and $3$-Regular
Compositions . . . . . . . . . . . . . . 16
M. A. Khan and
Harris Kwong On Sums of Products of Fibonacci-Type
Recurrences . . . . . . . . . . . . . . 20
Esther M. García-Caballero and
Samuel G. Moreno and
Michael P. Prophet New Vi\`ete-Like Infinite Products of
Nested Radicals with Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 27
Mihai Caragiu and
Alexandru Zaharescu and
Mohammad Zaki On Ducci Sequences with Primes . . . . . 32
H. Sedaghat Zero-Avoiding Solutions of the Fibonacci
Recurrence Modulo a Prime . . . . . . . 39
Kyle Fox and
William B. Kinnersley and
Daniel McDonald and
Nathan Orlow and
Gregory J. Puleo Spanning Paths in Fibonacci-Sum Graphs 46
Takao Komatsu Some Generalized Fibonacci Identities
Including Powers and Binomial
Coefficients . . . . . . . . . . . . . . 50
Linus Lindroos and
Andrew Sills and
Hua Wang Odd Fibbinary Numbers and the Golden
Ratio . . . . . . . . . . . . . . . . . 61
Burghard Herrmann The Golden Sequence . . . . . . . . . . 66
Ana Paula Chaves and
Diego Marques A Diophantine Equation Related to the
Sum of Squares of Consecutive
$k$-Generalized Fibonacci Numbers . . . 70
Peter J. Larcombe and
Eric J. Fennessey A Non-Linear Identity for a Particular
Class of Polynomial Families . . . . . . 75
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 80
Florian Luca Advanced Problems and Solutions . . . . 87
N. J. A. Sloane $ 2178 $ And All That . . . . . . . . . 99
Arthur T. Benjamin and
Curtis R. Heberle Counting on $r$-Fibonacci Numbers . . . 121
Kunle Adegoke The Golden Ratio, Fibonacci Numbers and
BBP-Type Formulas . . . . . . . . . . . 129--138
Toshio Nakata Another Probabilistic Proof of a
Binomial Identity . . . . . . . . . . . 139
Thomas Koshy Polynomial Extensions of the Lucas and
Ginsburg Identities . . . . . . . . . . 141
Lenny Jones and
Maria Markovich Generating Composite Sequences by
Appending Digits to Special Types of
Integers . . . . . . . . . . . . . . . . 148
Tauno Metsänkylä Note on Kummer's Congruences for Euler
Numbers . . . . . . . . . . . . . . . . 160
Kritkhajohn Onphaeng and
Prapanpong Pongsriiam Subsequences and Divisibility by Powers
of the Fibonacci Numbers . . . . . . . . 163
Martin W. Bunder Products and Powers, Powers and
Exponentiations, \ldots . . . . . . . . 172
Peter J. Larcombe and
Ovidiu D. Bagdasar and
Eric J. Fennessey On a Result of Bunder Involving Horadam
Sequences: A New Proof . . . . . . . . . 175
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 178
Florian Luca Advanced Problems and Solutions . . . . 185
Charles K. Cook RIT Redux . . . . . . . . . . . . . . . 194
Clark Kimberling Fusion, Fission, and Factors . . . . . . 195
Andreas N. Philippou A Note on the Modes of the Poisson
Distribution of Order $k$ . . . . . . . 203
Douglas Bowman Fibonacci Contractions of Continued
Fractions . . . . . . . . . . . . . . . 206
Pascal Ochem and
Michaël Rao Another Remark on the Radical of an Odd
Perfect Number . . . . . . . . . . . . . 215
Martin Griffiths Some Identities via Geometric Series . . 218
Donald M. Davis $p$-Adic Stirling Numbers of the Second
Kind . . . . . . . . . . . . . . . . . . 226
Peter J. Larcombe and
Sam T. O'Neill and
Eric J. Fennessey On Certain Series Expansions of the Sine
Function: Catalan Numbers and
Convergence . . . . . . . . . . . . . . 236
Russell Euler and
Jawad Sadek On a Generalized Pell Equation and a
Characterization of the Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 243
Philippe Demontigny and
Thao Do and
Archit Kulkarni and
Steven J. Miller and
Umang Varma A Generalization of Fibonacci
Far-Difference Representations and
Gaussian Behavior . . . . . . . . . . . 247
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 274
Florian Luca Advanced Problems and Solutions . . . . 281
Shanta Laishram and
Florian Luca Fibonacci Numbers of the Form $ x a \pm
x b \pm 1 $ . . . . . . . . . . . . . . 290
Eric F. Bravo and
Jhon J. Bravo and
Florian Luca Coincidences in Generalized Lucas
Sequences . . . . . . . . . . . . . . . 296
Kevin Hare and
Helmut Prodinger and
Jeffrey Shallit Three Series for the Generalized Golden
Mean . . . . . . . . . . . . . . . . . . 307
John Blythe Dobson On the Andrews Congruence for the
Fibonacci Quotient . . . . . . . . . . . 314
Jenica Cr\^\inganu On Approximating Euler's Constant . . . 318
Michael D. Hirschhorn Stirling Without Wallis . . . . . . . . 321
Andrzej P. Kisielewicz Some Binomial Identities Arising From a
Partition of an $n$-Dimensional Cube . . 325
Martin Griffiths Fixed-Term Zeckendorf Representations 331
Charles K. Cook and
Michael R. Bacon Some Polygonal Number Summation Formulas 336
Shane Chern and
Alvin Cui Fibonacci Numbers Close to a Power of 2 344
Peter J. Larcombe and
Eric J. Fennessey Conditions Governing Cross-Family Member
Equality in a Particular Class of
Polynomial Families . . . . . . . . . . 349
Kunle Adegoke A New Binary BBP-Type Formula for $
\sqrt{5} \log \phi $ . . . . . . . . . . 357--359
D. J. Grubb Factoring Chebyshev Polynomials . . . . 360
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 374
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Cover page . . . . . . . . . . . . . . . i
Anonymous Introduction . . . . . . . . . . . . . . iii
Anonymous Foreword . . . . . . . . . . . . . . . . v
Marjorie Bicknell-Johnson The Fibonacci Association: Historical
Snapshots . . . . . . . . . . . . . . . 1
Clark Kimberling and
Problem Editor Problem Proposals . . . . . . . . . . . 5
Peter G. Anderson More Properties of the Zeckendorf Array 15
Krassimir T. Atanassov and
Daryl R. DeFord and
Anthony G. Shannon Pulsated Fibonacci Recurrences . . . . . 22
Arthur T. Benjamin and
Elizabeth Reiland Combinatorial Proofs of Fibonomial
Identities . . . . . . . . . . . . . . . 28
Andrew Best and
Patrick Dynes and
Xixi Edelsbrunner and
Brian McDonald and
Steven J. Miller and
Kimsy Tor and
Caroline Turnage-Butterbaugh and
Madeleine Weinstein Benford Behavior of Zeckendorf
Decompositions . . . . . . . . . . . . . 35
Andrew Best and
Patrick Dynes and
Xixi Edelsbrunner and
Brian McDonald and
Steven J. Miller and
Kimsy Tor and
Caroline Turnage-Butterbaugh and
Madeleine Weinstein Gaussian Behavior of the Number of
Summands in Zeckendorf Decompositions in
Small Intervals . . . . . . . . . . . . 47
Daniel Birmajer and
Juan B. Gil and
Michael D. Weiner Convolutions of Tribonacci,
Fuss--Catalan, and Motzkin Sequences . . 54
Jens-P. Bode and
Heiko Harborth Steinhaus Triangles with Generalized
Pascal Addition . . . . . . . . . . . . 61
Minerva Catral and
Pari Ford and
Pamela Harris and
Steven J. Miller and
Dawn Nelson Generalizing Zeckendorf's Theorem: The
Kentucky Sequence . . . . . . . . . . . 68
Curtis Cooper Algebraic Statements Similar to Those in
Ramanujan's ``\booktitleLost Notebook'' 91
Daryl DeFord Enumerating Distinct Chessboard Tilings 102
M. Cetin Firengiz and
Naim Tuglu On the $q$-Seidel Matrix . . . . . . . . 117
Russell Jay Hendel A Cayley--Hamilton and Circulant
Approach to Jump Sums . . . . . . . . . 124
Clark Kimberling and
Peter J. C. Moses The Infinite Fibonacci Tree and Other
Trees Generated by Rules . . . . . . . . 136
Takao Komatsu and
Zuzana Masáková and
Edita Pelantová Higher-Order Identities for Fibonacci
Numbers . . . . . . . . . . . . . . . . 150
Florian Luca and
Pantelimon St\uanic\ua On Fibonacci Numbers which are Elliptic
Korselt Numbers . . . . . . . . . . . . 164
Sam Northshield Three Analogues of Stern's Diatomic
Sequence . . . . . . . . . . . . . . . . 168
G. K. Panda and
A. K. Panda Balancing-like Sequences Associated with
Integral Standard Deviations of
Consecutive Natural Numbers . . . . . . 187
Pantelimon St\uanic\ua Normic Continued Fractions in Totally
and Tamely Ramified Extensions of Local
Fields . . . . . . . . . . . . . . . . . 193
William Webb and
Nathan Hamlin Compositions and Recurrences . . . . . . 201
Paul Thomas Young Symmetries of Stirling Number Series . . 205
Yifan Zhang and
George Grossman Diophantine Triples and the
Extendibility of $ \{ 1, 2, 5 \} $, $ \{
1, 5, 10 \} $ . . . . . . . . . . . . . 212
Lawrence Somer and
Michal K\vrí\vzek On Primes in Lucas Sequences . . . . . . 2
Nathan Hamlin and
Bala Krishnamoorthy and
William Webb A Knapsack-Like Code Using Recurrence
Sequence Representations . . . . . . . . 24
Patrick Flanagan and
Marc S. Renault and
Josh Updike Symmetries of Fibonacci Points, Mod $m$ 34
Michael D. Hirschhorn A Connection Between $ \pi $ and $ \Phi
$ . . . . . . . . . . . . . . . . . . . 42
Michael D. Hirschhorn Ramanujan's Last Problem . . . . . . . . 48
Gábor Nyul and
Bettina Rauf On the Existence of van der Waerden Type
Numbers For Linear Recurrence Sequences
with Constant Coefficients . . . . . . . 53
Martin Griffiths and
William Wynn-Thomas A Property of a Fibonacci Staircase . . 61
Russell A. Gordon and
Sara L. Graham Comments on Proofs That There are No
Four Squares in Arithmetic Progression 68
Helmut Prodinger Two Families of Series for the
Generalized Golden Ratio . . . . . . . . 74
Philippe Ellia and
Paolo Menegatti Ramanujan--Nagell Type Equations and
Perfect Numbers . . . . . . . . . . . . 78
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 81
Florian Luca Advanced Problems and Solutions . . . . 88
Anonymous The John Riordan Prize . . . . . . . . . 96
Abdullah Al-Shaghay and
Karl Dilcher Congruences for Partial Sums of
Reciprocals . . . . . . . . . . . . . . 98
Russell Jay Hendel Quasi-Periods for the Hofstadter $Q$
Function . . . . . . . . . . . . . . . . 112
Alan Filipin The Extendibility of $ D(4) $-Pair $ \{
F_{2k}, 5 F_{2k} \} $ . . . . . . . . . 124
Kimmo Berg and
János Flesch and
Frank Thuijsman Golden and Silver Ratios in Bargaining 130
Thomas Koshy Graph-Theoretic Models for the
Univariate Fibonacci Family . . . . . . 135
Martin Griffiths and
Alex Bramham The Jacobsthal Numbers: Two Results and
Two Questions . . . . . . . . . . . . . 147
Stéphane Legendre Labeled Fibonacci Trees . . . . . . . . 152
Masayoshi Kaneda Two Remarks on the Collatz Cycle
Conjecture . . . . . . . . . . . . . . . 168
Peter J. Larcombe and
Eric J. Fennessey A Condition for Anti-Diagonals Product
Invariance Across Powers of $ 2 \times 2
$ Matrix Sets Characterizing a
Particular Class of Polynomial Families 175
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 180
Florian Luca Advanced Problems and Solutions . . . . 186
Neil J. A. Sloane The John Riordan Prize . . . . . . . . . 192
Christian Ballot Divisibility of Fibonomials and
Lucasnomials via A General Kummer Rule 194
Lawrence Somer and
Michal Krízek On Lehmer Superpseudoprimes . . . . . . 206
Corey Martinsen and
Pantelimon Stanica Asymptotic Behavior of Gaps Between
Roots of Weighted Factorials . . . . . . 213
Helmut Prodinger and
Stephan Wagner On Identities by Larcombe--Fennessey and
Cassini . . . . . . . . . . . . . . . . 219
L. Hajdu and
M. Szikszai Common Factors in Series of Consecutive
Terms of Associated Lucas and Lehmer
Sequences . . . . . . . . . . . . . . . 221
Martin Griffiths The Zeckendorf Representation of a
Beatty-Related Fibonacci Sum . . . . . . 230
James Alexander and
Paul Hearding A Graph-Theoretic Encoding of Lucas
Sequences . . . . . . . . . . . . . . . 237
Thomas Koshy Differences of Gibonacci Products with
the Same Order . . . . . . . . . . . . . 241
Russell Jay Hendel Coefficient Convergence of Recursively
Defined Polynomials . . . . . . . . . . 247
Peter J. Larcombe Closed Form Evaluations of Some Series
Comprising Sums of Exponentiated
Multiples of Two-Term and Three-Term
Catalan Number Linear Combinations . . . 253
G. K. Panda and
Ravi Kumar Davala Perfect Balancing Numbers . . . . . . . 261
Luis A. Medina and
Eric Rowland $p$-Regularity of the $p$-Adic Valuation
of the Fibonacci Sequence . . . . . . . 265
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 272
Florian Luca Advanced Problems and Solutions . . . . 279
Lawrence Somer and
Michal Krízek Identically Distributed Second-Order
Linear Recurrences Modulo $p$ . . . . . 290
M. Lawrence Glasser and
Yajun Zhou An Integral Representation for the
Fibonacci Numbers and Their
Generalization . . . . . . . . . . . . . 313
Michael D. Hirschhorn Binomial Identities and Congruences for
Euler Numbers . . . . . . . . . . . . . 319
R. S. Melham On Certain Families of Finite Reciprocal
Sums that Involve Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 323
Russell Euler and
Jawad Sadek An Extension of the Periodicity of an
Extended Fibonacci Family . . . . . . . 335
Thomas Koshy Gibonomial Coefficients with Interesting
Byproducts . . . . . . . . . . . . . . . 340
Victor H. Moll and
Christophe Vignat Generalized Bernoulli Numbers and a
Formula of Lucas . . . . . . . . . . . . 349
Peter J. Larcombe A Note on the Invariance of the General
$ 2 \times 2 $ Matrix Anti-Diagonals
Ratio with Increasing Matrix Power: Four
Proofs . . . . . . . . . . . . . . . . . 360
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 365
Florian Luca Advanced Problems and Solutions . . . . 372
Anonymous Volume Index . . . . . . . . . . . . . . 378
Clark Kimberling and
László Szalay $t$-sion of Two Polynomial Sequences and
Factorization Properties . . . . . . . . 3
Mahadi Ddamulira and
Florian Luca and
Mihaja Rakotomalala Fibonacci Numbers Which are Products of
Two Pell Numbers . . . . . . . . . . . . 11
R. S. Melham On a Classical Fibonacci Identity of
Aurifeuille . . . . . . . . . . . . . . 19
David Treeby Hidden Formulas in Fibonacci Tilings . . 23
R. S. Melham More New Algebraic Identities and the
Fibonacci Summations Derived From Them 31
Daniel López-Aguayo and
Florian Luca Sylvester's Theorem and the
Non-Integrality of a Certain Binomial
Sum . . . . . . . . . . . . . . . . . . 44
R. S. Melham On a Generalized Pell Equation Studied
by Euler and Sadek . . . . . . . . . . . 49
Jeremy F. Alm and
Taylor Herald A Note on Prime Fibonacci Sequences . . 55
Amin Witno Niven Repunits in General Bases . . . . 59
Michael A. Brilleslyper and
Nathan Wakefield and
A. J. Wallerstein and
Bradley Warner Comparing the Growth of the Prime
Numbers to the Natural Numbers . . . . . 65
David Garth and
Joseph Palmer Self-Similar Sequences and Generalized
Wythoff Arrays . . . . . . . . . . . . . 72
Tom Edgar Extending Some Fibonacci--Lucas
Relations . . . . . . . . . . . . . . . 79
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 80
Florian Luca Advanced Problems and Solutions . . . . 87
Anonymous Book Review: \booktitleThe Magic of
Math: Solving for $x$ and Figuring out
Why . . . . . . . . . . . . . . . . . . 94
José L. Ramírez The Pascal Rhombus and the Generalized
Grand Motzkin Paths . . . . . . . . . . 99
Charles K. Cook and
Takao Komatsu Some Identities for Sequences of
Binomial Sums of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 105
R. S. Melham A Two Parameter Pell Diophantine
Equation That Generalizes a Fibonacci
Classic . . . . . . . . . . . . . . . . 112
Carlo Sanna The $p$-Adic Valuation of Lucas
Sequences . . . . . . . . . . . . . . . 118
Nour-Eddine Fahssi Some Identities Involving Polynomial
Coefficients . . . . . . . . . . . . . . 125
Helmut Prodinger Determinants Containing Rising Powers of
Fibonacci Numbers . . . . . . . . . . . 137
Thomas Koshy Vieta Polynomials and Their Close
Relatives . . . . . . . . . . . . . . . 141
Spiros D. Dafnis and
Andreas N. Philippou Infinite Sums of Weighted Fibonacci
Numbers of Order $k$ . . . . . . . . . . 149
R. S. Melham Two Algebraic Identities and the
Alternating Fibonacci Sums Produced By
Them . . . . . . . . . . . . . . . . . . 154
Russell Euler and
Jawad Sadek A Direct Proof That $ F_n $ Divides $
F_{mn} $ Extended to Divisibility
Properties of Related Numbers . . . . . 160
Gaurav Bhatnagar Analogues of a Fibonacci--Lucas Identity 166
Serge Perrine Some Properties of the Equation $ x^2 =
5 y^2 - 4 $ . . . . . . . . . . . . . . 172
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 178
Florian Luca Advanced Problems and Solutions . . . . 185
Charles K. Cook Caen and Cheese: A Report on the
Seventeenth International Conference on
Fibonacci Numbers and Their Applications 194
R. S. Melham Closed Forms for Finite Sums in Which
the Denominator of the Summand is a
Product of Trigonometric Functions . . . 196
Rachel K. Graves and
Michael R. Bacon and
Charles K. Cook Using Matrices to Derive Identities for
Recursive Sequences . . . . . . . . . . 204
Lawrence Somer and
Michal K\vrí\vzek Identically Distributed Second-Order
Linear Recurrences Modulo $p$, II . . . 217
K. Liptai and
G. K. Panda and
L. Szalay A Balancing Problem on a Binary
Recurrence and its Associate . . . . . . 235
Peter J. Larcombe and
Eric J. Fennessey On a Scaled Balanced-Power Product
Recurrence . . . . . . . . . . . . . . . 242
R. S. Melham On the Positive Integer Points of
Certain Two Parameter Families of
Hyperbolas . . . . . . . . . . . . . . . 247
Steven Edwards and
William Griffiths A Combinatorial Identity Related to
Cross Polytope Numbers . . . . . . . . . 253
Peter J. Larcombe On the Evaluation of Sums of
Exponentiated Multiples of Generalized
Catalan Number Linear Combinations Using
a Hypergeometric Approach . . . . . . . 259
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 271
Florian Luca Advanced Problems and Solutions . . . . 280
Anonymous Winners of the Paul Bruckman Prize . . . 287
Anonymous The Paul Bruckman Prize . . . . . . . . 288
Anonymous Thanks and Welcome . . . . . . . . . . . 290
Jose Arnaldo B. Dris and
Florian Luca A Note on Odd Perfect Numbers . . . . . 291
R. S. Melham New Identities Satisfied by Powers of
Fibonacci and Lucas Numbers . . . . . . 296
Ronald P. Nordgren On Franklin and Complete Magic Square
Matrices . . . . . . . . . . . . . . . . 304
Zai-Qiao Bai and
Steven R. Finch Fibonacci and Lucas Representations . . 319
David Treeby Further Physical Derivations of
Fibonacci Summations . . . . . . . . . . 327
Alex Bramham and
Martin Griffiths Combinatorial Interpretations of Some
Convolution Identities . . . . . . . . . 335
Aram Tangboonduangjit and
Thotsaporn Thanatipanonda Determinants of Rising Powers of Second
Order Linear Recurrence Entries by Means
of the Desnanot--Jacobi Identity . . . . 340
Helmut Prodinger Additional Results on Some Recent
Infinite Sums . . . . . . . . . . . . . 344
Minerva Catral and
Pari L. Ford and
Pamela E. Harris and
Steven J. Miller and
Dawn Nelson Legal Decompositions Arising From
Non-Positive Linear Recurrences . . . . 348
Russ Euler and
Jawad Sadek Elementary Problems and Solutions . . . 366
Florian Luca Advanced Problems and Solutions . . . . 373
Anonymous Paul Bruckman Prize . . . . . . . . . . 380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Andreas M. Hinz The Lichtenberg Sequence . . . . . . . . 2
Thomas Koshy and
Zhenguang Gao Polynomial Extensions of a Diminnie
Delight . . . . . . . . . . . . . . . . 13
Chatchawan Panraksa and
Aram Tangboonduangjit On Some Arithmetic Properties of a
Sequence Related to the Quotient of
Fibonacci Numbers . . . . . . . . . . . 21
Prapanpong Pongsriiam Fibonacci and Lucas Numbers Which are
One Away From Their Products . . . . . . 29
Roberto B. Corcino and
Hassan Jolany and
Cristina B. Corcino and
Takao Komatsu On Generalized Multi Poly-Euler
Polynomials . . . . . . . . . . . . . . 41
Petros Hadjicostas and
Lingyun Zhang Sommerville's Symmetrical Cyclic
Compositions of a Positive Integer with
Parts Avoiding Multiples of an Integer 54
Andrew Bulawa and
Whan Ki Lee Integer Values of Generating Functions
for the Fibonacci and Related Sequences 74
Harris Kwong Elementary Problems and Solutions . . . 82
Florian Luca Advanced Problems and Solutions . . . . 89
Anonymous Paul Bruckman Prize . . . . . . . . . . 96
Anonymous Fibonacci Conference Announcement . . . 98
R. S. Melham Closed Forms for Finite Sums of Weighted
Products of Generalized Fibonacci
Numbers . . . . . . . . . . . . . . . . 99
Danielle Cox and
Karyn McLellan A Problem on Generation Sets Containing
Fibonacci Numbers . . . . . . . . . . . 105
Ralph P. Grimaldi Extraordinary Subsets: A Generalization 114
R. S. Melham Closed Forms for Finite Sums of Weighted
Products of the Sine and Cosine
Functions . . . . . . . . . . . . . . . 123
Thomas Koshy and
Ralph P. Grimaldi Ternary Words and Jacobsthal Numbers . . 129
Mark Bryant and
David Hobill Golden-Ratio-Based Rectangular Tilings 137
Thomas Koshy Polynomial Extensions of the Lucas and
Ginsburg Identities Revisited . . . . . 147
Chad Davis and
Daniel Eloff and
Blair K. Spearman Normal Integral Bases of a Cyclic
Quintic Field . . . . . . . . . . . . . 152
Raphael Schumacher The Self-Counting Identity . . . . . . . 157
Peter J. Larcombe and
Eric J. Fennessey A Closed Form Formulation for the
General Term of a Scaled Triple Power
Product Recurrence Sequence . . . . . . 168
Harris Kwong Elementary Problems and Solutions . . . 178
Florian Luca Advanced Problems and Solutions . . . . 184
Anonymous Paul Bruckman Prize . . . . . . . . . . 192
Anonymous Fibonacci Conference and Caen
Proceedings Announcements . . . . . . . 194
R. S. Melham Closed Forms for Certain Fibonacci Type
Sums That Involve Second Order Products 195
Charles K. Cook and
Michael R. Bacon and
Rebecca A. Hillman Higher Order Boustrophedon Transforms
for Certain Well-Known Sequences . . . . 201
Lawrence Somer and
Michal Krízek On Moduli for Which Certain Second-Order
Linear Recurrences Contain a Complete
System of Residues Modulo $m$ . . . . . 209
R. S. Melham Sums of Certain Products of Fibonacci
and Lucas Numbers --- Part III . . . . . 229
Yifan Zhang and
George Grossman A Combinatorial Proof for the Generating
Function of Powers of the Fibonacci
Sequence . . . . . . . . . . . . . . . . 235
Henrik Eriksson and
Markus Jonsson Level Sizes of the Bulgarian Solitaire
Game Tree . . . . . . . . . . . . . . . 243
Minerva Catral and
Pari L. Ford and
Pamela E. Harris and
Steven J. Miller and
Dawn Nelson and
Zhao Pan and
Huanzhong Xu New Behavior in Legal Decompositions
Arising from Non-Positive Linear
Recurrences . . . . . . . . . . . . . . 252
Harris Kwong Elementary Problems and Solutions . . . 276
Florian Luca Advanced Problems and Solutions . . . . 282
Anonymous Paul Bruckman Prize . . . . . . . . . . 288
Anonymous Fibonacci Conference and Caen
Proceedings Announcements . . . . . . . 290
Márton Szikszai Distinct Products in Lucas Sequences ---
On a Problem of Kimberling . . . . . . . 291
Christian Ballot Divisibility of the Middle Lucasnomial
Coefficient . . . . . . . . . . . . . . 297
A. K. Panda and
G. K. Panda Circular Balancing Numbers . . . . . . . 309
Russell Euler and
Jawad Sadek Relationships Between $k$-Gonal Numbers
that Are Centered $k$-Gonal, and Lucas
and Related Numbers . . . . . . . . . . 315
Thomas Koshy and
Zhenguang Gao Polynomial Extensions of a Diminnie
Delight Revisited: Part I . . . . . . . 320
Mihai Caragiu and
Paul A. Vicol and
Mohammad Zaki On Conway's Subprime Function, A
Covering of $N$ and an Unexpected
Appearance of the Golden Ratio . . . . . 327
Ovidiu D. Bagdasar and
Peter J. Larcombe On the Masked Periodicity of Horadam
Sequences: A Generator-Based Approach 332
Gábor Nyul and
Gabriella Rácz Lucas Sequences and the Hosoya Index of
Graphs . . . . . . . . . . . . . . . . . 340
Kunle Adegoke Some Infinite Product Identities
Involving Fibonacci and Lucas Numbers 343
Filip Saidak The Prime Numbers Without the Sieve of
Eratosthenes . . . . . . . . . . . . . . 352
Steven Edwards and
William Griffiths Generalizations of Delannoy and Cross
Polytope Numbers . . . . . . . . . . . . 357
Harris Kwong Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 374
Anonymous Paul Bruckman Prize . . . . . . . . . . 380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Jean-Paul Allouche Some Extremalities of the Binary
Fibonacci Sequence . . . . . . . . . . . ??
Peter G. Anderson Notes & Extensions for a Remarkable
Continued Fraction . . . . . . . . . . . ??
Anonymous Conference Report . . . . . . . . . . . ??
Anonymous Foreword . . . . . . . . . . . . . . . . ??
Anonymous List of Participants . . . . . . . . . . ??
Anonymous Title page . . . . . . . . . . . . . . . ??
Christian Ballot and
Clark Kimberling and
Peter J. C. Moses Linear Recurrences Originating From
Polynomial Trees . . . . . . . . . . . . ??
Arthur T. Benjamin and
Joel Ornstein A Bijective Proof of a Derangement
Recurrence . . . . . . . . . . . . . . . ??
Bruce M. Boman and
Thien-Nam Dinh and
Keith Decker and
Brooks Emerick and
Christopher Raymond and
Gilberto Schleiniger Why do Fibonacci Numbers Appear in
Patterns of Growth in Nature? . . . . . ??
Christopher Brown The Natural Logarithm of the Golden
Section . . . . . . . . . . . . . . . . ??
Zvonko Cerin On Candido Like Identities . . . . . . . ??
Curtis Cooper and
Steven Miller and
Peter J. C. Moses and
Murat Sahin and
Thotsaporn Thanatipanonda On Identities of Ruggles, Horadam,
Howard, and Young . . . . . . . . . . . ??
Paul Cull What I Tell You $K$ Times is True . . . ??
Russell Jay Hendel Proof and Generalization of the
Cassini--Catalan--Tagiuri--Gould
Identities . . . . . . . . . . . . . . . ??
Virginia P. Johnson and
Charles K. Cook Areas of Triangles and Other Polygons
with Vertices from Various Sequences . . ??
Clark Kimberling Problem Proposals . . . . . . . . . . . ??
Tamás Lengyel On the Rate of $p$-adic Convergence of
Alternating Sums of Powers of Binomial
Coefficients . . . . . . . . . . . . . . ??
Ray Li and
Steven J. Miller A Collection of Central Limit Type
Results in Generalized Zeckendorf
Decompositions . . . . . . . . . . . . . ??
Frédéric Mansuy Fibonacci words and the construction of
a ``Quasicrystalline'' Fivefold
Structure . . . . . . . . . . . . . . . ??
Steven J. Miller and
Dawn Nelson and
Zhao Pan and
Huanzhong Xu On the Asymptotic Behavior of Variance
of PLRS Decompositions . . . . . . . . . ??
Augustine O. Munagi Two Applications of the Bijection on
Fibonacci Set Partitions . . . . . . . . ??
Claudio Pita Ruiz Weighted Sums of Squares via Generalized
Eulerian Polynomials . . . . . . . . . . ??
Gabriela N. Stanica and
Pantelimon Stanica Recurrences for Entries of Powers of
Matrices . . . . . . . . . . . . . . . . ??
Paul K. Stockmeyer An Exploration of Sequence A000975 . . . ??
Tamás Szakács $k$-Order Linear Recursive Sequences and
the Golden Ratio . . . . . . . . . . . . ??
Mohammed Taous On the 2-Class Group of $ \mathbb
{Q}(\bar {5 p F_p}) $ Where $ F_p $ is a
Prime Fibonacci Number . . . . . . . . . 192--200
Paul Thomas Young Congruences for Bernoulli--Lucas Sums ??
Anonymous Fibonacci Conference and Caen
Proceedings Announcements . . . . . . . 2
R. S. Melham Further Closed Forms for Finite Sums of
Weighted Products of Generalized
Fibonacci Numbers . . . . . . . . . . . 3
Thomas Koshy and
Zhenguang Gao Polynomial Extensions of a Diminnie
Delight Revisited: Part II . . . . . . . 10
Murat Sahin and
Elif Tan Conditional (Strong) Divisibility
Sequences . . . . . . . . . . . . . . . 18
Michael D. Hirschhorn Congruences Modulo 5 for Partitions Into
at Most Four Parts . . . . . . . . . . . 32
R. S. Melham Further Closed Forms for Finite Sums of
Weighted Products of the Sine and Cosine
Functions . . . . . . . . . . . . . . . 38
Ji\vrí Kla\vska Donald Dines Wall's Conjecture . . . . . 43
Bernadette Faye and
Florian Luca On $X$-Coordinates of Pell Equations
that Are Repdigits . . . . . . . . . . . 52
Salah Eddine Rihane and
Mohand Ouamar Hernane and
Alain Togbé On the $ D(4) $-Diophantine Triples of
Fibonacci Numbers . . . . . . . . . . . 63
Martin Griffiths A Formula for an Infinite Family of
Fibonacci-Word Sequences . . . . . . . . 75
Harris Kwong Elementary Problems and Solutions . . . 81
Florian Luca Advanced Problems and Solutions . . . . 89
Anonymous Paul Bruckman Prize . . . . . . . . . . 96
Anonymous Fibonacci Conference and Final
Announcement . . . . . . . . . . . . . . 98
R. S. Melham Sums of Reciprocals of Weighted Products
of the Sine and and Cosine Functions . . 99
Thomas Koshy Polynomial Extensions of the Lucas and
Ginsburg Identities Revisited:
Additional Dividends I . . . . . . . . . 106
Michael Debellevue and
Ekaterina Kryuchkova Fractal Behavior of the Fibonomial
Triangle Modulo Prime $p$, Where the
Rank of Apparition of $p$ is $ p + 1$ 113
Peter J. Larcombe and
Sam T. O'Neill A Generating Function Approach to the
Automated Evaluation of Sums of
Exponentiated Multiples of Generalized
Catalan Number Linear Combinations . . . 121
Florian Luca and
Anitha Srinivasan Markov Equation With Fibonacci
Components . . . . . . . . . . . . . . . 126
Matthew E. Coppenbarger Iterations of a Modified Sisyphus
Function . . . . . . . . . . . . . . . . 130
Russell Jay Hendel Towards Formulating a Tagiuri Generating
Method Conjecture . . . . . . . . . . . 142
Roger C. Alperin $A$-Cassini Sequences and Their Spectrum 153
Mark D. LaDue Clusters of Integers With Equal Total
Stopping Times in the $ 3 X + 1 $
Problem . . . . . . . . . . . . . . . . 156
Paul Dalenberg and
Tom Edgar Consecutive Factorial Base Niven Numbers 163
R. S. Melham Closed Formulas for Finite Sums of
Weighted Fractional Generalized
Fibonacci Products . . . . . . . . . . . 167
Harris Kwong Elementary Problems and Solutions . . . 177
Florian Luca Advanced Problems and Solutions . . . . 185
Anonymous Paul Bruckman Prize . . . . . . . . . . 192
Marjorie Bicknell-Johnson A Report on the 18th International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 194
Clark Kimberling and
Takao Komatsu and
Kálmán Liptai and
László Szalay A Connection Between Hyper-Fibonacci
Numbers and Fissions of Polynomial
Sequences . . . . . . . . . . . . . . . 195
John Greene Lucas Sequences and Traces of Matrix
Products . . . . . . . . . . . . . . . . 200
Thomas Koshy Differences of Gibonacci Polynomial
Products of Orders 2, 3, and 4 . . . . . 212
Helen G. Grundman and
Pamela E. Harris Sequences of Consecutive Happy Numbers
in Negative Bases . . . . . . . . . . . 221
Dmitriy Shtefan and
Irina Dobrovolska The Sums of the Consecutive Fibonacci
Numbers . . . . . . . . . . . . . . . . 229
Thomas Koshy and
Martin Griffiths Some Gibonacci Convolutions with
Dividends . . . . . . . . . . . . . . . 237
Manasi Kumari Sahukar and
G. K. Panda Arithmetic Functions of Balancing
Numbers . . . . . . . . . . . . . . . . 246
Kunle Adegoke Weighted Sums of Some Second-Order
Sequences . . . . . . . . . . . . . . . 252
Robert Frontczak Some Fibonacci--Lucas--Tribonacci--Lucas
Identities . . . . . . . . . . . . . . . 263
Harris Kwong Elementary Problems and Solutions . . . 275
Florian Luca Advanced Problems and Solutions . . . . 283
Anonymous Paul Bruckman Prize . . . . . . . . . . 288
R. S. Melham Closed Forms for 10 Families of Finite
Sums of Fractional Generalized Fibonacci
Products . . . . . . . . . . . . . . . . 290
Kritkhajohn Onphaeng and
Prapanpong Pongsriiam The Converse of Exact Divisibility by
Powers of the Fibonacci and Lucas
Numbers . . . . . . . . . . . . . . . . 296
Brian Hopkins and
Aram Tangboonduangjit Fibonacci-Producing Rational Polynomials 303
Ulrich Abel Some New Identities for Derangement
Numbers . . . . . . . . . . . . . . . . 313
S. G. Rayaguru and
G. K. Panda Repdigits as Products of Consecutive
Balancing or Lucas-Balancing Numbers . . 319
Bir Kafle and
Florian Luca and
Alain Togbé Triangular Repblocks . . . . . . . . . . 325
R. S. Melham 12 Two-Parameter Families of Reciprocal
Sums of Products of the Sine and Cosine
Functions . . . . . . . . . . . . . . . 329
Andreas N. Philippou and
Spiros D. Dafnis A Simple Proof of an Identity
Generalizing Fibonacci--Lucas Identities 334
Sheng-Liang Yang and
Yuan-Yuan Gao The Pascal Rhombus and Riordan Arrays 337
Chatchawan Panraksa and
Aram Tangboonduangjit $p$-adic Valuation of Lucas Iteration
Sequences . . . . . . . . . . . . . . . 348
Santos Hernández Hernández The Fibonacci Numbers of the Form $ 2^a
\pm 2^b + 1 $ . . . . . . . . . . . . . 354
R. S. Melham Closed Formulas for Finite Sums of
Fractional Expressions That Involve the
Sine and Cosine Functions . . . . . . . 360
Alan F. Beardon Fibonacci Matrices . . . . . . . . . . . 363
Harris Kwong Elementary Problems and Solutions . . . 366
Florian Luca Advanced Problems and Solutions . . . . 373
Anonymous Paul Bruckman Prize . . . . . . . . . . 380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Fibonacci Conference Announcement . . . 2
R. Ben Taher and
H. Benkhaldoun Solving the linear difference equation
with periodic coefficients via Fibonacci
sequences . . . . . . . . . . . . . . . 2549--2564
Sajed Haque and
Jeffrey Shallit A Class of Exponential Sequences with
Shift-Invariant Discriminators . . . . . 3
Peter J. Larcombe and
Eric J. Fennessey A Non-Linear Recurrence Identity Class
for Terms of a Generalized Linear
Recurrence Sequence of Degree Three . . 10
Roger C. Alperin $A$-Cassini Polynomial Sequences and
Applications . . . . . . . . . . . . . . 14
Laurent Habsieger Explicit Bounds for the Diophantine
Equation $ A! B! = C! $ . . . . . . . . 21
Arthur T. Benjamin and
Joshua Crouch and
James A. Sellers Unified Tiling Proofs of a Family of
Fibonacci Identities . . . . . . . . . . 29
Ryan Zielinski Faulhaber and Bernoulli . . . . . . . . 32
Atsanon Wadsanthat and
Chatchawan Panraksa Distribution of Cycle Lengths of a
Quadratic Map Over Finite Fields of
Characteristic 2 . . . . . . . . . . . . 35
Juan B. Gil and
Aaron Worley Generalized Metallic Means . . . . . . . 45
Lenny Jones and
Lawrence Somer Primefree Shifted Binary Linear
Recurrence Sequences . . . . . . . . . . 51
Sergiy Koshkin Non-classical Linear Divisibility
Sequences and Cyclotomic Polynomials . . 68
Harris Kwong Elementary Problems and Solutions . . . 81
Florian Luca Advanced Problems and Solutions . . . . 89
Anonymous Paul Bruckman Prize . . . . . . . . . . 96
Anonymous Fibonacci Conference Announcement . . . 98
Thomas Koshy Jacobsthal and Jacobsthal--Lucas Walks 99
Alexandre Gueganic and
Granger Carty and
Yujin H. Kim and
Steven J. Miller and
Alina Shubina and
Shannon Sweitzer and
Eric Winsor and
Jianing Yang Limiting Distributions in Generalized
Zeckendorf Decompositions . . . . . . . 109
Saralee Aursukaree and
Tammatada Khemaratchatakumthorn and
Prapanpong Pongsriiam Generalizations of Hermite's Identity
and Applications . . . . . . . . . . . . 126
M. K. Sahukar and
G. K. Panda Repdigits in Euler Functions of Pell
Numbers . . . . . . . . . . . . . . . . 134
Thomas Koshy A Recurrence for Gibonacci Cubes with
Graph-Theoretic Confirmations . . . . . 139
Owen J. Brison and
J. Eurico Nogueira Linear Recurring Sequence Subgroups in
the Complex Field --- II . . . . . . . . 148
Elen Viviani Pereira Spreafico and
Mustapha Rachidi Fibonacci Fundamental System and
Generalized Cassini Identity . . . . . . 155
Raphael Schumacher How to Sum the Squares of the Tetranacci
Numbers and the Fibonacci $m$-Step
Numbers . . . . . . . . . . . . . . . . 168
Harris Kwong Elementary Problems and Solutions . . . 176
Florian Luca Advanced Problems and Solutions . . . . 184
Anonymous Paul Bruckman Prize . . . . . . . . . . 192
Anonymous Fibonacci Conference Announcement . . . 194
Éric Angelini and
Lars Blomberg and
Charlie Neder and
Rémy Sigrist and
N. J. A. Sloane ``Choix de Bruxelles'': A New Operation
on Positive Integers . . . . . . . . . . 195
Eric Chen and
Robin Chen and
Lucy Guo and
Cindy Jiang and
Steven J. Miller and
Joshua M. Siktar and
Peter Yu Gaussian Behavior in Zeckendorf
Decompositions from Lattices . . . . . . 201
Ray Li and
Steven J. Miller Central Limit Theorems for Gaps of
Generalized Zeckendorf Decompositions 213
Sai Gopal Rayaguru and
Gopal Krishna Panda Repdigits as Products of Balancing and
Lucas-Balancing Numbers With Indices in
Arithmetic Progression . . . . . . . . . 231
Taras Goy and
Roman Zatorsky On Oresme Numbers and Their Connection
with Fibonacci and Pell Numbers . . . . 238
Montree Jaidee and
Prapanpong Pongsriiam Arithmetic Functions of Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 246
Florian Luca and
Sibusiso Mabaso Diophantine Equations with the Ramanujan
$ \tau $ Function of Factorials,
Fibonacci Numbers, and Catalan Numbers 255
Masakazu Yamagishi A Short Proof of Congruences for Lucas
Sequences . . . . . . . . . . . . . . . 260
Christian Ballot The $p$-adic Valuation of Lucas
Sequences When $p$ Is a Special Prime 265
Harris Kwong Elementary Problems and Solutions . . . 276
Florian Luca Advanced Problems and Solutions . . . . 283
Anonymous Paul Bruckman Prize . . . . . . . . . . 288
Anonymous Fibonacci Conference Announcement . . . 290
Steven J. Tedford Combinatorial Identities for the Padovan
Numbers . . . . . . . . . . . . . . . . 291
Shiran Rachmilevitch Alternating Offers Bargaining and the
Golden Ratio . . . . . . . . . . . . . . 299
Thomas Koshy Some Extended Gibonacci Polynomial Sums
with Dividends . . . . . . . . . . . . . 303
Helmut Prodinger and
Sarah J. Selkirk Sums of Squares of Tetranacci Numbers: A
Generating Function Approach . . . . . . 313
Roger C. Alperin A Family of Nonlinear Recurrences and
Their Linear Solutions . . . . . . . . . 318
Thomas Koshy and
Zhenguang Gao Periodicity of Ones Digits in Jacobsthal
Numbers with Triangular and Jacobsthal
Subscripts . . . . . . . . . . . . . . . 322
Ben Delo and
Filip Saidak Euclid's Theorem Redux . . . . . . . . . 331
Lin Yang and
Sheng-Liang Yang The Parametric Pascal Rhombus . . . . . 337
Steven J. Tedford Fibonacci Graphs . . . . . . . . . . . . 347
Gopal Krishna Panda and
Sushree Sangeeta Pradhan Triangular-Like Numbers That Are
Triangular . . . . . . . . . . . . . . . 356
Alaa Altassan and
Florian Luca On a Curious Property of $ F_{184} $ . . 363
Christian Ballot Errata --- The $p$-adic Valuation of
Lucas Sequences When $p$ Is a Special
Prime . . . . . . . . . . . . . . . . . 366
Harris Kwong Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 373
Anonymous Paul Bruckman Prize . . . . . . . . . . 380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Marjorie Bicknell-Johnson Conference Report . . . . . . . . . . . i
Paul Baird-Smith and
Alyssa Epstein and
Kristen Flint and
Steven J. Miller The Generalized Zeckendorf Game . . . . 1
Matthew Blair and
Rigoberto Flórez and
Antara Mukherjee Matrices in the Hosoya Triangle . . . . 15
Bruce M. Boman and
Yihan Ye and
Keith Decker and
Christopher Raymond and
Gilberto Schleiniger Geometric Branching Patterns based on
$p$-Fibonacci Sequences: Self-similarity
Across Different Degrees of Branching
and Multiple Dimensions . . . . . . . . 29
Curtis Cooper Some High Degree Generalized Fibonacci
Identities . . . . . . . . . . . . . . . 42
Kenneth Edwards and
Michael A. Allen A new combinatorial interpretation of
the Fibonacci numbers squared . . . . . 48
Russell Jay Hendel Proof of the Tagiuri Histogram
Conjecture . . . . . . . . . . . . . . . 54
Burghard Herrmann How Integer Sequences Find Their Way
Into Areas Outside Pure Mathematics . . 67
Andreas M. Hinz and
Paul K. Stockmeyer Discovering Fibonacci Numbers, Fibonacci
Words, and a Fibonacci Fractal in the
Tower of Hanoi . . . . . . . . . . . . . 72
Lin Jiu and
Christophe Vignat Connection Coefficients for Higher-order
Bernoulli and Euler Polynomials: A
Random Walk Approach . . . . . . . . . . 84
Clark Kimberling and
Peter J. C. Moses Linear Complementary Equations and
Systems . . . . . . . . . . . . . . . . 96
Sam Northshield $ \Re^3 $ counting the Rationals . . . . 111--129
Prapanpong Pongsriiam Fibonacci and Lucas Numbers which have
Exactly Three Prime Factors and Some
Unique Properties of $ F_{18} $ and $
L_{18} $ . . . . . . . . . . . . . . . . 130
Thotsaporn ``Aek'' Thanatipanonda Statistics of Domino Tilings on a
Rectangular Board . . . . . . . . . . . 145
Paul Thomas Young Global series for zeta functions . . . . 154
Clark Kimberling Problem Section . . . . . . . . . . . . 170
Anonymous Fibonacci Conference Announcement . . . 2
Asim Patra and
G. K. Panda Positive Integer Solutions of Some
Diophantine Equations Involving
Lucas-Balancing Numbers . . . . . . . . 3
Mahadi Ddamulira On the $x$-Coordinates of Pell Equations
That Are Products of Two Lucas Numbers 18
F. Michel Dekking Base Phi Representations and Golden Mean
Beta-Expansions . . . . . . . . . . . . 38
César Bautista-Ramos and
Carlos Guillén-Galván and
Paulino Gómez-Salgado Independence Polynomials of Fibonacci
Trees Are Log-Concave . . . . . . . . . 49
Lawrence Somer and
Michal K\vrí\vzek Iteration of Certain Arithmetical
Functions of Particular Lucas Sequences 55
Rigoberto Flòrez and
Robinson A. Higuita Another Proof for Partial Strong
Divisibility Property of Lucas-Type
Polynomials . . . . . . . . . . . . . . 70
João Lita da Silva On Some Linear Recurrences . . . . . . . 73
Saralee Aursukaree and
Tammatada Khemaratchatakumthorn and
Prapanpong Pongsriiam Corrigendum to Generalizations of
Hermite's Identity and Applications . . 80
Harris Kwong Elementary Problems and Solutions . . . 81
Florian Luca Advanced Problems and Solutions . . . . 89
Anonymous Paul Bruckman Prize . . . . . . . . . . 96
Anonymous Fibonacci Conference Announcement . . . 98
Jonathan J. Azose and
Arthur T. Benjamin A Tiling Interpretation of the
$q$-Binomial Coefficients . . . . . . . 99
Bruno Dular Cycles of Sums of Integers . . . . . . . 126
Roger C. Alperin A Nonlinear Recurrence and Its Relations
to Chebyshev Polynomials . . . . . . . . 140
Neelima Borade and
Dexter Cai and
David Z. Chang and
Bruce Fang and
Alex Liang and
Steven J. Miller and
Wanqiao Xu Gaps of Summands of the Zeckendorf
Lattice . . . . . . . . . . . . . . . . 143
Steven J. Miller and
Alexandra Newlon The Fibonacci Quilt Game . . . . . . . . 157
Kenneth Edwards and
Michael A. Allen A New Combinatorial Interpretation of
the Fibonacci Numbers Squared. Part II 169
Harris Kwong Elementary Problems and Solutions . . . 178
Florian Luca Advanced Problems and Solutions . . . . 185
Anonymous The Paul Bruckman Prize . . . . . . . . 192
Raphael Schumacher Explicit Formulas for Sums Involving the
Squares of the First $n$ Tribonacci
Numbers . . . . . . . . . . . . . . . . 194
Anton Shutov On the Sum of Digits of the Zeckendorf
Representations of Two Consecutive
Numbers . . . . . . . . . . . . . . . . 203
Evan Fang and
Jonathan Jenkins and
Zack Lee and
Daniel Li and
Ethan Lu and
Steven J. Miller and
Dilhan Salgado and
Joshua M. Siktar Central Limit Theorems for Compound
Paths on the Two-Dimensional Lattice . . 208
Bir Kafle and
Anitha Srinivasan and
Alain Togbé Markoff Equation with Pell Components 226
Daniel Larsen Focusing Sequences and Self-Similarity 231
Thomas Koshy Extended Gibonacci Sums of Polynomial
Products of Order $3$ . . . . . . . . . 241
H\`ung Vi\dêt Chu and
Steven J. Miller and
Zimu Xiang Higher Order Fibonacci Sequences from
Generalized Schreier Sets . . . . . . . 249
Salah Eddine Rihane and
Bernadette Faye and
Florian Luca and
Alain Togbé Powers of Two in Generalized Lucas
Sequences . . . . . . . . . . . . . . . 254
Berit Givens and
Victor H. Moll Integrals of Fibonacci Polynomials and
Their Valuations . . . . . . . . . . . . 261
Harris Kwong Elementary Problems and Solutions . . . 274
Florian Luca Advanced Problems and Solutions . . . . 281
Anonymous The Paul Bruckman Prize . . . . . . . . 288
Marjorie Bicknell Johnson A Report on the 19th International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 290
Thomas Koshy and
Zhenguang Gao Extended Gibonacci Sums of Polynomial
Products of Order 3 Revisited . . . . . 291
Robert Davis and
Greg Simay Further Combinatorics and Applications
of Two-toned Tilings . . . . . . . . . . 300
Muharem Avdispahi\'c and
Faruk Zejnulahi An Integer Sequence with a Divisibility
Property . . . . . . . . . . . . . . . . 321
Richard J. McIntosh Congruences Involving Euler Numbers and
Power Sums . . . . . . . . . . . . . . . 328
H\`ung Vi\.êt Chu Representation of $ \frac {1}{2}(F_n -
1)(F_{n + 1} - 1) $ and $ \frac
{1}{2}(F_n - 1)(F_{n + 2} - 1) $ . . . . 334
Jathan Austin and
Lisa Schneider Generalized Fibonacci Sequences in
Pythagorean Triple Preserving Matrices 340
H\`ung Vi\.ê Chu and
Lân Khánh Chu A Twist of a Ramanujan Identity . . . . 351
Pankaj Jyoti Mahanta and
Manjil P. Saikia A Family of Lacunary Recurrences for
Lucas Numbers . . . . . . . . . . . . . 356
Takao Komatsu and
Paul Thomas Young Convolutions of Generalized Stirling
Numbers and Degenerate Bernoulli
Polynomials . . . . . . . . . . . . . . 361
Harris Kwong Elementary Problems and Solutions . . . 367
Florian Luca Advanced Problems and Solutions . . . . 375
Anonymous Paul Bruckman Prize . . . . . . . . . . 380
Anonymous Volume Index . . . . . . . . . . . . . . 381
Marjorie Bicknell-Johnson Conference Report . . . . . . . . . . . 1
Santiago Alzate and
Oscar Correa and
Rigoberto Flórez Fibonacci Identities from Jordan
Identities . . . . . . . . . . . . . . . 2
Peter G. Anderson The Fibonacci Word as a 2-adic Number
and its Continued Fraction . . . . . . . 21
Bob Bastasz Lyndon Words of a Second-Order
Recurrence . . . . . . . . . . . . . . . 25
Arthur T. Benjamin and
John Lentfer and
Thomas C. Martinez Counting on Euler and Bernoulli Number
Identities . . . . . . . . . . . . . . . 30
Matthew Blair and
Rigoberto Flórez and
Antara Mukherjee and
José L. Ramírez Matrices in the Determinant Hosoya
Triangle . . . . . . . . . . . . . . . . 34
El\.zbieta Bo\ldyriew and
Anna Cusenza and
Linglong Dai and
Pei Ding and
Aidan Dunkelberg and
John Haviland and
Kate Huffman and
Dianhui Ke and
Daniel Kleber and
Jason kuretski and
John Lentfer and
Tianhao Luo and
Steven J. Miller and
Clayton Mizgerd and
Vashisth Tiwari and
Jingkai Ye and
Yunhao Zhang and
Xiaoyan Zheng and
Weiduo Zhu Extending Zeckendorf's Theorem to a
Non-constant Recurrence and the
Zeckendorf Game on this Non-constant
Recurrence Relation . . . . . . . . . . 55
El\.zbieta Bo\ldyriew and
John Haviland and
Phúc Lâm and
John Lentfer and
Steven J. Miller and
Fernando Trejos Suárez An Introduction to Completeness of
Positive Linear Recurrence Sequences . . 77
Bruce M. Boman Geometric Capitulum Patterns Based on
Fibonacci p-Proportions . . . . . . . . 91
Zakariae Bouazzaoui On Periods of Fibonacci Sequences and
Real Quadratic $p$-rational Fields . . . 103
Spiros D. Dafnis On the Relation Between Fibonacci and
Lucas Numbers . . . . . . . . . . . . . 111
Daniel Duverney and
Yohei Tachiya Linear Independence of Infinite Products
Generated by the Lucas Numbers . . . . . 115
Kenneth Edwards and
Michael A. Allen A New Combinatorial Interpretation of
the Fibonacci Numbers Cubed . . . . . . 128
Russell Jay Hendel Recursive Triangles Appearing Embedded
in Recursive Families . . . . . . . . . 135
Burghard Herrmann The Continued Fraction Pendulum . . . . 144
Ruoci Li and
Xiaonan Li and
Steven J. Miller and
Clayton Mizgerd and
Chenyang Sun and
Dong Xia and
Zhyi Zhou Deterministic Zeckendorf Games . . . . . 152
Augustine O. Munagi An Identity for Inverse-Conjugate
Compositions . . . . . . . . . . . . . . 161
Kouichi Nakagawa A Triangle with Sides Lengths of a
Rational Power of the Plastic Constant 166
Sam Northshield Topographs; Conway and Otherwise . . . . 172
R. L. Ollerton and
A. G. Shannon A Note on Brousseau's Summation Problem 190
Genki Shibukawa New Identities for Some Symmetric
Polynomials, and a Higher Order Analogue
of the Fibonacci and Lucas Numbers . . . 200
Anitha Srinivasan The Markoff--Fibonacci Numbers . . . . . 222
Kai Wang Girard--Waring Type Formula for a
Generalized Fibonacci Sequence . . . . . 229
Steven J. Miller Problem Section . . . . . . . . . . . . 236
Anonymous In Memoriam --- Gerald E. Bergum . . . . 2
Anonymous Fibonacci Conference Announcement . . . 3
Thomas Koshy Extended Gibonacci Sums of Polynomial
Products of Orders 4 and 5 . . . . . . . 3
Kendra Killpatrick and
Jordan Weaver A Bijection for the Fibonomial
Coefficients . . . . . . . . . . . . . . 14
F. Michel Dekking How to Add Two Natural Numbers in Base
Phi . . . . . . . . . . . . . . . . . . 19
Thomas Koshy Extended Gibonacci Sums of Polynomial
Products of Orders 4 and 5 Revisited . . 23
Saralee Aursukaree and
Prapanpong Pongsriiam On Exactly $3$-Deficient-Perfect Numbers 33
A. G. Shannon and
R. L. Ollerton A Note on Ledin's Summation Problem . . 47
Asim Patra and
Gopal Krishna Panda and
Tammatada Khemaratchatakumthorn Exact Divisibility by Powers of the
Balancing and Lucas-Balancing Numbers 57
Yao-Qiang Li Divisibility Properties of Factors of
the Discriminant of Generalized
Fibonacci Numbers . . . . . . . . . . . 65
Xianzu Lin Values of Bernoulli and Euler
Polynomials at Rational Points . . . . . 78
Harris Kwong Elementary Problems and Solutions . . . 82
Florian Luca Advanced Problems and Solutions . . . . 89
Thomas Koshy A Family of Sums of Gibonacci Polynomial
Products of Order 4 . . . . . . . . . . 98
Lawrence Somer and
Michal K\vrí\vzek Second-Order Linear Recurrences Having
Arbitrarily Large Defect Modulo $p$ . . 108
H\`ung Vi\dêt Chu Partial Sums of the Fibonacci Sequence 132
Mark Broderius and
John Greene Lucas Sequences Containing Few Primes 136
José Luis Cereceda Bernoulli and Faulhaber . . . . . . . . 145
Sergi Elizalde A Simple Bijective Proof of a Familiar
Derangement Recurrence . . . . . . . . . 150
H\`ung Vi\dêt Chu Various Sequences from Counting Subsets 152
Yuji Tsuno Extended Results on Integer Values of
the Generating Functions for Sequences
Given by Pell's Equations . . . . . . . 158
Thomas Koshy Graph-Theoretic Confirmations of Four
Sums of Gibonacci Polynomial Products of
Order 4 . . . . . . . . . . . . . . . . 167
Harris Kwong Elementary Problems and Solutions . . . 176
Florian Luca Advanced Problems and Solutions . . . . 185
E. L. Roettger and
H. C. Williams Some Primality Tests Constructed from a
Cubic Extension of the Lucas Functions 194
Seán M. Stewart Some Series Involving Products Between
the Harmonic Numbers and the Fibonacci
Numbers . . . . . . . . . . . . . . . . 214
Thomas Koshy A Family of Sums of Gibonacci Polynomial
Products of Order 4 Revisited . . . . . 225
Helmut Prodinger Nondecreasing Deutsch Paths . . . . . . 232
Thomas Koshy Infinite Sums Involving Gibonacci
Polynomial Products . . . . . . . . . . 237
Hans J. H. Tuenter Inverse Relations for Lucas Sequences 246
H\`ung Vi\dêt Chu On Generalized Zeckendorf Decompositions
and Generalized Golden Strings . . . . . 254
Thomas Koshy Infinite Sums Involving Gibonacci
Polynomial Products Revisited . . . . . 262
Richard L. Ollerton and
Anthony G. Shannon Erratum --- Some Properties of
Generalized Pascal Squares and Triangles 272
Harris Kwong Elementary Problems and Solutions . . . 273
Florian Luca Advanced Problems and Solutions . . . . 280
Anonymous Fibonacci Conference Announcement . . . 290
Glenn J. Fox Integers that Satisfy a Fermat's
Congruence of Higher Power . . . . . . . 291
Florian Luca On the Discriminant of the
$k$-generalized Fibonacci Polynomial . . 298
Anna Cusenza and
Aidan Dunkelberg and
Kate Huffman and
Dianhui Ke and
Daniel Kleber and
Steven J. Miller and
Clayton Mizgerd and
Vashisth Tiwari and
Jingkai Ye and
Xiaoyan Zheng Winning Strategy for Multiplayer and
Multialliance Zeckendorf Games . . . . . 308
Thomas Koshy Graph-Theoretic Confirmations of Four
Sums of Jacobsthal Polynomial Products
of Order 4 . . . . . . . . . . . . . . . 319
Amelia Gilson and
Hadley Killen and
Tamás Lengyel and
Steven J. Miller and
Nadia Razek and
Joshua M. Siktar and
Liza Sulkin Zeckendorf's Theorem Using Indices in an
Arithmetic Progression . . . . . . . . . 327
Thomas Koshy Infinite Sums Involving Jacobsthal
Polynomial Products . . . . . . . . . . 338
Soowhan Yoon Analytic Connection Between the
Fibonacci Sequence and Diagonal Sums of
Binomial Coefficients . . . . . . . . . 349
Iwan Praton and
Nart Shalqini Amicable Heron Triangles . . . . . . . . 362
Harris Kwong Elementary Problems and Solutions . . . 365
Florian Luca Advanced Problems and Solutions . . . . 373
Anonymous Volume Index . . . . . . . . . . . . . . 381
Anonymous Fibonacci Conference Announcement . . . 2
Thomas Koshy Infinite Sums Involving Jacobsthal
Polynomial Products Revisited . . . . . 3
Thomas Koshy Products Involving Reciprocals of
Gibonacci Polynomials . . . . . . . . . 15
Kouessi Norbert Adédji and
Alan Filipin and
Alain Togbé On the Family of Diophantine Pairs $
P_{2 k}, 2 P_{2 k + 2} $ . . . . . . . . 25
Patrick Moss and
Tom Ward Fibonacci Along Even Powers Is (Almost)
Realizable . . . . . . . . . . . . . . . 40
Mohammad Javaheri Upper Bound Residues of the Fibonacci
Sequence Modulo Primes . . . . . . . . . 48
Abigail Hoit An Asymptotic Upper Bound for Counting
Fiven Numbers . . . . . . . . . . . . . 52
Anna Cusenza and
Aidan Dunkelberg and
Kate Huffman and
Dianhui Ke and
Micah McClatchey and
Steven J. Miller and
Clayton Mizgerd and
Vashisth Tiwari and
Jingkai Ye and
Xiaoyan Zheng Bounds on Zeckendorf Games . . . . . . . 57
Thomas Koshy Products Involving Reciprocals of
Jacobsthal Polynomials . . . . . . . . . 72
Harris Kwong Elementary Problems and Solutions . . . 82
Florian Luca Advanced Problems and Solutions . . . . 90
Anonymous Fibonacci Conference Announcement . . . 98
Ziqian (Alexa) Jin and
Greg Dresden Tetranacci Identities Via Hexagonal
Tilings . . . . . . . . . . . . . . . . 99
Thomas Koshy Infinite Sums Involving Gibonacci
Polynomials . . . . . . . . . . . . . . 104
H\`ung Vi\dêt Chu and
David C. Luo and
Steven J. Miller On Zeckendorf Related Partitions Using
the Lucas Sequence . . . . . . . . . . . 111
Thomas Koshy Infinite Sums Involving Gibonacci
Polynomials Revisited . . . . . . . . . 120
Greg Dresden and
Yu Xiao Weighted Sums of Fibonacci and Lucas
Numbers Through Colorful Tilings . . . . 126
Paul Kinlaw and
Michael Morris and
Samanthak Thiagarajan Sums Related to the Fibonacci Sequence 136
Russell Jay Hendel A Method for Uniformly Proving a Family
of Identities . . . . . . . . . . . . . 151
George E. Andrews and
Matthew Just and
Greg Simay Anti-Palindromic Compositions . . . . . 158
Harris Kwong Elementary Problems and Solutions . . . 177
Florian Luca Advanced Problems and Solutions . . . . 185
Thomas Koshy Infinite Sums Involving Jacobsthal
Polynomials . . . . . . . . . . . . . . 194
Max A. Alekseyev and
Joseph Samuel Myers and
Richard Schroeppel and
S. R. Shannon and
N. J. A. Sloane and
Paul Zimmermann Three Cousins of Recamán's Sequence . . . 201
H. E. A. Campbell and
D. L. Wehlau Zigzag Sequences and Representations of
Integers . . . . . . . . . . . . . . . . 220
Helmut Prodinger A Matrix with Sums of Catalan Numbers
--- $ L U $-Decomposition and
Determinant . . . . . . . . . . . . . . 226
Thomas Koshy Infinite Sums Involving Jacobsthal
Polynomials Revisited . . . . . . . . . 229
A. F. Beardon Ratios of Generalized Fibonacci Numbers 235
R. L. Ollerton Catalan Numbers and Non-Intersecting
Lattice Paths . . . . . . . . . . . . . 238
Alexandru Gica Congruences Modulo the Square of a Prime
for Sums Containing Fibonacci Numbers 243
John M. Campbell A Matrix-Based Recursion Relation for $
F_{F_n} $ . . . . . . . . . . . . . . . 256
Wojciech Guzicki and
Piotr Zakrzewski Bijective Proofs of Formulas with $ ( -
1)^n $ . . . . . . . . . . . . . . . . . 262
John M. Campbell Products of Multiple-Index Fibonacci
Numbers . . . . . . . . . . . . . . . . 267
Harris Kwong Elementary Problems and Solutions . . . 274
Florian Luca Advanced Problems and Solutions . . . . 281
Marjorie Bicknell Johnson In Memoriam --- Fredric T. Howard . . . 290
Marjorie Bicknell Johnson A Report on the 20th International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 291
Thomas Koshy Infinite Sums Involving Extended
Gibonacci Polynomials . . . . . . . . . 292
Thomas Koshy Infinite Sums Involving Extended
Gibonacci Polynomials Revisited . . . . 302
Hans J. H. Tuenter Fibonacci Summation Identities Arising
from Catalan's Identity . . . . . . . . 312
John Greene and
Junhyun Lim and
Shaunak Mashalkar and
Edward F. Schaefer Using Fibonacci Factors to Create
Fibonacci Pseudoprimes . . . . . . . . . 320
Lawrence Somer and
Michal K\vrí\vzek Frobenius, Lucas, and Dickson
Pseudoprimes . . . . . . . . . . . . . . 325
Thomas Koshy Sums Involving Gibonacci Polynomials . . 344
Kevin Beanland and
H\`ung Vi\dêt Chu and
Carrie E. Finch-Smith Generalized Schreier Sets, Linear
Recurrence Relation, and Turán Graphs . . 352
Lawrence Somer and
Michal K\vrí\vzek Generalization of a Theorem of Bruckman
on Dickson Pseudoprimes . . . . . . . . 357
Paul C. Kainen Fibonacci in Somos-5 by Complexification 362
Harris Kwong Elementary Problems and Solutions . . . 365
Robert Frontczak and
Florian Luca Advanced Problems and Solutions . . . . 373
Marjorie Bicknell-Johnson Conference Report . . . . . . . . . . . 1
Anonymous List of Speakers and Talks . . . . . . . 2
Michael A. Allen and
Kenneth Edwards Fence Tiling Derived Identities
Involving the Metallonacci Numbers
Squared or Cubed . . . . . . . . . . . . 5
Benjamin Baily and
Justine Dell and
Irfan Durmi\'c and
Henry L. Fleischmann and
Faye Jackson and
Isaac Mijares and
Steven J. Miller and
Ethan Pesikoff and
Luke Reifenberg and
Alicia Smith Reina and
Yingzi Yang The Bergman Game . . . . . . . . . . . . 18
Amine Belkhir and
Elif Tan and
Mehmet Da\uglì Some Combinatorial Aspects of
Bi-periodic Incomplete Horadam Sequences 39
Arthur T. Benjamin and
Daniela Elizondo Counting on Hosoya's Triangle . . . . . 47
Hsin-Yun Ching and
Rigoberto Flórez and
F. Luca and
Antara Mukherjee and
J. C. Saunders Primes and Composites in the Determinant
Hosoya Triangle . . . . . . . . . . . . 56
Hao Cui and
Xiaoyu Cui and
Sophia C. Davis and
Irfan Durmi\'c and
Qingcheng Hu and
Lisa Liu and
Steven J. Miller and
Fengping Ren and
Alicia Smith Reina and
Eliel Sosis Sums of Reciprocals of Recurrence
Relations . . . . . . . . . . . . . . . 111
Robert Dougherty-Bliss The Meta-C-Finite Ansatz . . . . . . . . 143
Emily Evans and
Russell Jay Hendel An Infinite 2-Dimensional Array
Associated With Electric Circuits . . . 151
Russell Jay Hendel A System of Four Simultaneous
Recursions: Generalization of the
Ledin--Shannon--Ollerton Identity . . . 172
Brian Hopkins and
Aram Tangboonduangjit Verifying and Generalizing Arndt's
Compositions . . . . . . . . . . . . . . 181
Sergey Kirgizov $ \mathbb {Q} $-bonacci Words and
Numbers . . . . . . . . . . . . . . . . 187
Sergey Kirgizov and
José L. Ramírez Polyominoes and Graphs Built From
Fibonacci Words . . . . . . . . . . . . 196
Bahar Kulo\uglu and
Engin Özkan and
Anthony G. Shannon The Narayana Sequence in Finite Groups 212
Thomas C. Martinez and
Steven J. Miller and
Clayton Mizgerd and
Chenyang Sun Generalizing Zeckendorf's Theorem to
Homogeneous Linear Recurrences, I . . . 222
Thomas C. Martinez and
Steven J. Miller and
Clayton Mizgerd and
Jack Murphy and
Chenyang Sun Generalizing Zeckendorf's Theorem to
Homogeneous Linear Recurrences, II . . . 231
aBa Mbirika and
Jürgen Spilker GCD of Sums of $k$ Consecutive Squares
of Generalized Fibonacci Numbers . . . . 255
Steven J. Miller and
Eliel Sosis and
Jingkai Ye Winning Strategies for Generalized
Zeckendorf Games . . . . . . . . . . . . 270
Steven J. Miller and
Fei Peng and
Tudor Popescu and
Nawapan Wattanawanichkul Walking to Infinity on the Fibonacci
Sequence . . . . . . . . . . . . . . . . 293
Sam Northshield Some Generalizations of a Formula of
Reznick . . . . . . . . . . . . . . . . 299
Prasanta Kumar Ray and
Kisan Bhoi On the Diophantine equation $ N_n = x^a
\pm x^b + 1 $ . . . . . . . . . . . . . 316
Raphael Schumacher The Self-Counting Flow . . . . . . . . . 324
Lejla Smajlovi\'c and
Zenan \vSabanac and
Lamija \vS\'ceta On the Generalized Tribonacci Zeta
Function . . . . . . . . . . . . . . . . 344
Lejla Smajlovi\'c and
Zenan \vSabanac and
Lamija \vS\'ceta On the Hurwitz-Type Zeta Function
Associated to the Lucas Sequence . . . . 355
Earth Sonrod and
Kate Tanner and
Colin Leyner Some Properties of the Fibonacci--Pascal
Triangle . . . . . . . . . . . . . . . . 372
Pagdame Tiebekabe and
Isma\"\ila Diouf On the Diophantine equation $ F_{n_1} +
F_{n_2} + F_{n_3} + F_{n_4} + F_{n_5} =
2^a $ . . . . . . . . . . . . . . . . . 384
Steven J. Miller Problem Section . . . . . . . . . . . . 401
Anonymous Mathematics books for sale (as a
fundraiser) . . . . . . . . . . . . . . 403
Thomas Koshy Sums Involving Jacobsthal Polynomials 2
Thomas Koshy Additional Sums Involving Gibonacci
Polynomials . . . . . . . . . . . . . . 12
Michael A. Allen and
Kenneth Edwards Identities Involving the Tribonacci
Numbers Squared Via Tilings with Combs 21
Xander Faber and
Jon Grantham On Integers Whose Sum Is the Reverse of
Their Product . . . . . . . . . . . . . 28
Thomas Koshy Additional Sums Involving Gibonacci
Polynomials: Graph-Theoretic
Confirmations . . . . . . . . . . . . . 42
William Paulsen Calkin--Wilf Sequences for Irrational
Numbers . . . . . . . . . . . . . . . . 51
Thomas Koshy Additional Sums Involving Gibonacci
Polynomials Revisited . . . . . . . . . 60
Kou\`essi Norbert Adédji and
Alan Filipin and
Salah Eddine Rihane and
Alain Togbé Fibonacci or Lucas Numbers That Are
Concatenations of Two g-Repdigits . . . 68
Harris Kwong Elementary Problems and Solutions . . . 84
Robert Frontczak Advanced Problems and Solutions . . . . 91
Thomas Koshy Sums Involving Gibonacci Polynomial
Squares . . . . . . . . . . . . . . . . 98
Michel Dekking and
Ad van Loon On the Representation of the Natural
Numbers by Powers of the Golden Mean . . 105
Thomas Koshy Sums Involving Gibonacci Polynomial
Squares: Graph-theoretic Confirmations 119
Harold R. Parks and
Dean C. Wills Sums of $k$-Bonacci Numbers . . . . . . 129
Thomas Koshy Sums Involving Jacobsthal Polynomial
Squares . . . . . . . . . . . . . . . . 135
John M. Campbell Sums of Fibonacci Numbers Indexed by
Integer Parts . . . . . . . . . . . . . 143
Thomas Koshy Sums Involving Gibonacci Polynomial
Squares Revisited . . . . . . . . . . . 153
King Shun Leung $ \phi $-Expansions of Rationals . . . . 162
Passawan Noppakaew and
Pavita Kanwarunyu and
Parit Wanitchatchawan $k$-Fibonacci Numbers and $k$-Lucas
Numbers in Beatty Sequences Generated by
Powers of Metallic Means . . . . . . . . 167
Harris Kwong Elementary Problems and Solutions . . . 178
Robert Frontczak Advanced Problems and Solutions . . . . 185
H\`ung Vi\.êt Chu A Note on the Fibonacci Sequence and
Schreier-Type Sets . . . . . . . . . . . 194
Thomas Koshy Sums Involving Gibonacci Polynomial
Squares: Generalizations . . . . . . . . 197
Thomas Koshy Additional Sums Involving Gibonacci
Polynomial Squares . . . . . . . . . . . 207
Jeffrey Shallit Some Tribonacci Conjectures . . . . . . 214
Thomas Koshy Additional Sums Involving Jacobsthal
Polynomial Squares . . . . . . . . . . . 222
Maciej Ulas Representing Generalized Derangements as
Sums of Three Squares . . . . . . . . . 231
Beno\^\it Rittaud Fibonacci-like Sequences for Variants of
the Tower of Hanoi, with Corresponding
Graphs and Gray Codes . . . . . . . . . 240
Guilherme Zeus Dantas E Moura and
Andrew Keisling and
Astrid Lilly and
Annika Mauro and
Steven J. Miller and
Matthew Phang and
Santiago Velazquez Iannuzzelli Recurrence Relations for $S$-Legal Index
Difference Sequences . . . . . . . . . . 257
Harris Kwong Elementary Problems and Solutions . . . 275
Robert Frontczak Advanced Problems and Solutions . . . . 282
Thomas Koshy Infinite Sums Involving Gibonacci
Polynomials Revisited: Generalizations 291
Florian Luca and
Japhet Odjoumani and
Alain Togbé Tribonacci Numbers That Are Products of
Two Fibonacci Numbers . . . . . . . . . 298
Thomas Koshy Infinite Sums Involving Jacobsthal
Polynomials: Generalizations . . . . . . 305
Thomas Koshy Sums Involving Two Classes of Gibonacci
Polynomials . . . . . . . . . . . . . . 312
Jathan Austin On Pythagorean Triple Preserving
Matrices That Contain Fibonacci Numbers 321
Thomas Koshy Sums Involving Two Classes of Gibonacci
Polynomials Revisited . . . . . . . . . 327
Thomas Koshy Additional Sums Involving Gibonacci
Polynomial Squares Revisited . . . . . . 334
Michael Nyblom Deleting Terms of the Divergent
$p$-Series and Reciprocals of Primes
Series Using the Thue--Morse Sequence 339
Thomas Koshy More Sums Involving Gibonacci Polynomial
Squares . . . . . . . . . . . . . . . . 346
Chance Sanford A Remark on Dedekind Sums and
Palindromic Continued Fractions . . . . 357
Hans J. H. Tuenter A Triple Fibonacci Sum and Some
Historical Notes . . . . . . . . . . . . 361
Harris Kwong Elementary Problems and Solutions . . . 367
Robert Frontczak Advanced Problems and Solutions . . . . 374
Anonymous Volume Index . . . . . . . . . . . . . . 382
Anonymous Fibonacci Conference Announcement . . . 2
Diego Garcia-Fernandezsesma and
Steven J. Miller and
Thomas Rascon and
Risa Vandegrift and
Ajmain Yamin The Accelerated Zeckendorf Game . . . . 3
Michael A. Jones and
Brittany C. Ohlinger Self-Similar Structure of $P$-Positions
of the Game Euclid . . . . . . . . . . . 15
Thomas Koshy More Sums Involving Gibonacci Polynomial
Squares Revisited . . . . . . . . . . . 29
Thomas Koshy Sums Involving a Class of Gibonacci
Polynomial Squares: Generalizations . . 34
Thomas Koshy and
Zhenguang Gao Sums Involving a Class of Jacobsthal
Polynomial Squares . . . . . . . . . . . 40
Andreea M. St\uanic\ua and
Gabriela N. St\uanic\ua and
Pantelimon St\uanic\ua An Evaluation of Rationally Weighted
Binomial Sums Via Some Differential and
Integral Operators . . . . . . . . . . . 45
John M. Campbell and
Emrah Kìlìç Binomial Sums Involving Second-Order
Linearly Recurrent Sequences . . . . . . 57
Joseph Tonien Fibonacci and Pi Squared . . . . . . . . 65--74
Thomas Koshy Sums Involving a Family of Gibonacci
Polynomial Squares: Generalizations . . 75
Harris Kwong Elementary Problems and Solutions . . . 84
Robert Frontczak Advanced Problems and Solutions . . . . 90
Anonymous Fibonacci Conference Announcement . . . 98
Anonymous Mathematics Books for Sale . . . . . . . 99
Maribel Diaz Noguera and
Rigoberto Flórez and
José L. Ramírez and
Martha Romero Rojas Catalan Identities for Generalized
Fibonacci Polynomials . . . . . . . . . 100
Michel Dekking and
Ad van Loon Counting Base Phi Representations . . . 112
Helen G. Grundman Closing an Open Problem on Negative Base
Happy Numbers . . . . . . . . . . . . . 125
Thomas Koshy and
Zhenguang Gao Sums Involving a Family of Jacobsthal
Polynomial Squares . . . . . . . . . . . 130
Nassima Belaggoun and
Hac\`ene Belbachir Combinatorial Identities for the
Bi-Periodic Fibonacci Numbers Squared 136
Yinqi Lin and
Bo Zhou Infinite Sums Involving Powers of
Gibonacci Polynomials . . . . . . . . . 147
Yuji Tsuno Polynomial Values with Integer
Coefficients for the Generating
Functions of Fibonacci Polynomials . . . 157
Harris Kwong Elementary Problems and Solutions . . . 173
Robert Frontczak Advanced Problems and Solutions . . . . 181
Marjorie Bicknell Johnson A Report on the 21st International
Conference on Fibonacci Numbers and
Their Applications . . . . . . . . . . . 190
Anonymous Mathematics Books for Sale . . . . . . . 192
Florian Luca On the Discriminant of the
$k$-Generalized Fibonacci Polynomial, II 193
Kantaphon Kuhapatanakul Note on the Generalized Leonardo Numbers 201
Christian Táfula Knights Are $ 24 / 13 $ Times Faster
than the King . . . . . . . . . . . . . 208
Éric Angelini and
Michael S. Branicky and
Giovanni Resta and
N. J. A. Sloane and
David W. Wilson The Comma Sequence: a Simple Sequence
with Bizarre Properties . . . . . . . . 215
Michael R. Bacon and
Charles K. Cook Some Properties of Oresme Numbers and
Convolutions with Various Second Order
Sequences . . . . . . . . . . . . . . . 233
Benjamin Earp-Lynch and
Simon Earp-Lynch and
Omar Kihel and
Puntani Pongsumpun Extension of the Equation $ \sum^k_{j =
1} j F_j^p = F_n^p $ to a Family of
Lucas Sequences . . . . . . . . . . . . 241
Harris Kwong Elementary Problems and Solutions . . . 258
Robert Frontczak Advanced Problems and Solutions . . . . 265
Haruo Iwasaki A New Classification of the Kaprekar
Numbers . . . . . . . . . . . . . . . . 275
Kálmán Liptai and
László Németh and
Tamás Szakács and
László Szalay On Certain Fibonacci Representations . . 282
Emily J. Evans and
Russell Jay Hendel Recursions and Characteristic
Polynomials of the Rows of the Circuit
Array . . . . . . . . . . . . . . . . . 290
H\`ung Vi\SGMLentity7879t Chu and
Zachary Louis Vasseur Weighted Schreier-type Sets and the
Fibonacci Sequence . . . . . . . . . . . 305
Florian Luca and
Makoko Campbell Manape On the Euler Function of Linearly
Recurrence Sequences . . . . . . . . . . 316
Harris Kwong Elementary Problems and Solutions . . . 329
Robert Frontczak Advanced Problems and Solutions . . . . 337
Anonymous Volume Index . . . . . . . . . . . . . . 345
Leopold Gegenbauer Bemerkung über Leonardo Pisano's
\booktitleliber Abaci. (German) [Remark
on Leonardo Pisano's \booktitleliber
Abaci] . . . . . . . . . . . . . . . . . 402
R. B. McClenon Leonardo of Pisa and his \booktitleLiber
Quadratorum . . . . . . . . . . . . . . 1--8
G. Loria Leonardo Fibonacci . . . . . . . . . . . 379--410
Ettore Carruccio L'estrazione di radice cubica, mediante
inserzione di due medie proporzionali
fra due segmenti dati, in Leonardo
Pisano. (Italian) [The extraction of the
cube root, by inserting two mean
proportions between two data segments,
in Leonardo of Pisa] . . . . . . . . . . 189--197
Attilio Frajese L'algebra geometrica in Leonardo Pisano.
(Italian) [The geometric algebra of
Leonardo Pisano] . . . . . . . . . . . . 363--365
L. S. Johnston The Fibonacci Sequence and Allied
Trigonometric Identities . . . . . . . . 85--89
José Babini On the linear systems of Leonardo Pisano 57--61
Irving Kaplansky Lucas's Tests for Mersenne Numbers . . . 188--190
Dov Jarden Two Theorems on Fibonacci's Sequence . . 425--427
Charles W. Raine Pythagorean triangles from the Fibonacci
series . . . . . . . . . . . . . . . . . 164
A. Agostini L'uso delle lettere nel \booktitleLiber
abaci di Leonardo Fibonacci. (Italian)
[The use of the letters in
\booktitleLiber abaci Leonardo
Fibonacci] . . . . . . . . . . . . . . . 282--287
Robert S. Beard The golden section and Fibonacci numbers 116--119
P. Schub A minor Fibonacci curiosity . . . . . . 214--214
G. Candido A relationship between the fourth powers
of the terms of the Fibonacci series . . 230--230
Carolyn Eisele The \booktitleLiber Abaci through the
eyes of Charles S. Peirce . . . . . . . 236--259
Amedeo Agostini Leonardo Fibonacci . . . . . . . . . . . 205--206
D. Block Curiosum # 330: Fibonacci summations . . 191--191
Daniel Block Symbolic formulae involving Fibonacci
numbers . . . . . . . . . . . . . . . . 306--307
K. Subba Rao Some Properties of Fibonacci Numbers . . 680--684
J. Ginsburg A relationship between cubes of
Fibonacci numbers . . . . . . . . . . . 242--242
Charles W. Raine Fibonacci equiareal triangles . . . . . 96--98
Raphael I. Reichman A summation formula involving Fibonacci
numbers . . . . . . . . . . . . . . . . 111--112
K. Subba Rao Some summation formulae involving
Fibonacci numbers . . . . . . . . . . . 214--217
J. H. Means Classroom Notes: Predetermined
Determinant Values Using Fibonacci
Numbers . . . . . . . . . . . . . . . . 657--658
Richard P. Kelisky On formulas involving both the Bernoulli
and Fibonacci numbers . . . . . . . . . 27--35
Richard P. Kelisky On formulas involving both the Bernoulli
and Fibonacci numbers . . . . . . . . . 27--35
Sam E. Ganis Classroom Notes: Notes on the Fibonacci
Sequence . . . . . . . . . . . . . . . . 129--130
David E. Ferguson Fibonaccian searching . . . . . . . . . 648--648
E. P. Miles, Jr. Generalized Fibonacci Numbers and
Associated Matrices . . . . . . . . . . 745--752
George Shapiro Mathematical Notes: Some Properties of
the Fibonacci Numbers . . . . . . . . . 876--876
D. D. Wall Fibonacci Series Modulo $m$ . . . . . . 525--532
A. F. Horadam Corrections: a Generalized Fibonacci
Sequence . . . . . . . . . . . . . . . . 637--637
A. F. Horadam Fibonacci Number Triples . . . . . . . . 751--753
A. F. Horadam A Generalized Fibonacci Sequence . . . . 455--459
M. L. Juncosa Letter to the Editor: concerning
Ferguson's paper on Fibonaccian
searching . . . . . . . . . . . . . . . 252--252
S. E. Mamangakis Mathematical Notes: Remarks on the
Fibonacci Series Modulo $m$ . . . . . . 648--649
Stephen Puckette Recent Publications: \em Popular
Lectures in Mathematics Series, Vol. 1
The Method of Mathematical Induction, by
I. S. Sominskii; \em Popular Lectures in
Mathematics Series, Vol. 2 Fibonacci
Numbers, by N. N. Vorob'ev; \em Popular
Lectures in Mathematics Series, Vol. 3
Some Applications of Mechanics to
Mathematics, by V. A. Uspenskii; \em
Popular Lectures in Mathematics Series,
Vol. 4 Geometrical Constructions Using
Compasses Only, by A. N. Kostovskii; \em
Popular Lectures in Mathematics Series,
Vol. 5 The Ruler in Geometrical
Constructions, by A. S. Smogorzhevskii;
\em Popular Lectures in Mathematics
Series, Vol. 6 Inequalities, by P. P.
Korovkin . . . . . . . . . . . . . . . . 1020--1020
S. L. Basin Generalized Fibonacci Sequences and
Squared Rectangles . . . . . . . . . . . 372--379
A. F. Horadam Mathematical Notes: Complex Fibonacci
Numbers and Fibonacci Quaternions . . . 289--291
P. Krolak and
L. Cooper An extension of Fibonaccian search to
several variables . . . . . . . . . . . 639--641
Dmitri Thoro Classroom Notes: Regula Falsi and the
Fibonacci Numbers . . . . . . . . . . . 869--869
M. Wunderlich On the Non-Existence of Fibonacci
Squares (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 455--457
David Zeitlin Classroom Notes: On Identities for
Fibonacci Numbers . . . . . . . . . . . 987--991
U. Alfred Mathematical Notes: Relation of Zeros to
Periods in the Fibonacci Sequence Modulo
a Prime . . . . . . . . . . . . . . . . 897--899
Floyd Buchanan Mathematical Notes: $ {N} $-th Powers in
the Fibonacci Series . . . . . . . . . . 647--649
Floyd Buchanan Mathematical Notes: Retraction of ``$
{N} $-th Powers in the Fibonacci
Series'' . . . . . . . . . . . . . . . . 1112--1112
Floyd Buchanan Mathematical Notes: $N$-th Powers in the
Fibonacci Series . . . . . . . . . . . . 647--649
P. J. Federico Mathematical Notes: a Fibonacci Perfect
Squared Square . . . . . . . . . . . . . 404--406
Sidney Kravitz and
Murray Berg Lucas' Test for Mersenne Numbers, $ 6000
< p < 7000 $ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 148--149
Joseph Arkin An Extension of the Fibonacci Numbers 275--279
D. M. Bloom On Periodicity in Generalized Fibonacci
Sequences . . . . . . . . . . . . . . . 856--861
M. Donald MacLaren and
George Marsaglia Uniform Random Number Generators . . . . 83--89
K. J. Overholt An Instability in the Fibonacci and
Golden Section Search Methods . . . . . 284--286
George N. Raney Generalization of the Fibonacci sequence
to $n$ dimensions . . . . . . . . . . . 332--349
Friedrich Gebhardt Generating Pseudo-Random Numbers by
Shuffling a Fibonacci Sequence (in
Technical Notes and Short Papers) . . . 708--709
K. J. Overholt Note on Algorithm 2: Fibonacci search 414--414
M. C. Pike and
I. D. Hill and
F. D. James Note on Algorithm 2: Fibonacci search,
and on Algorithm 7: MINX . . . . . . . . 416--417
Patrick D. Krolak Further extensions of Fibonaccian search
to nonlinear programming problems . . . 258--265
Gino Arrighi Il trattato di geometria e la
volgarizzazione del \booktitleLiber
quadratorum di Leonardo Pisano del
Codice Palatino 577 (sec XV) della
Biblioteca Nazionale di Firenze.
(Italian) [The treatise on geometry and
the vulgarization of the \booktitleLiber
quadratorum of Leonardo Pisano in the
Palatino Code 577 (XV century) the
National Library of Florence] . . . . . 760--775
Richard Barakat and
Elizabeth Baumann $M$ th Power of an $ N \times N $ Matrix
and Its Connection with the Generalized
Lucas Polynomials . . . . . . . . . . . 1474--1476
Hans Riesel Lucasian Criteria for the Primality of $
\mathcal {N} = h \cdot 2^n - 1 $ . . . . 869--875
Yehiel Ilamed Powers of a matrix and the generalized
Lucas polynomials . . . . . . . . . . . 113--113
M. D. Miller Mathematical Notes: On Generalized
Fibonacci Numbers . . . . . . . . . . . 1108--1109
L. Carlitz and
V. E. Hoggatt and
Richard Scoville Some functions related to Fibonacci and
Lucas representations . . . . . . . . . 71--102
J. Král Erratum: ``A new additive pseudorandom
number generator for extremely short
word-length'' . . . . . . . . . . . . . 216--216
J. Král A new additive pseudorandom number
generator for extremely short
word-length . . . . . . . . . . . . . . 164--167
I. V. V. Raghavacharyulu and
A. R. Tekumalla Solution of the difference equations of
generalized Lucas polynomials . . . . . 321--324
E. Zeckendorf Représentation des Nombres naturels par
une Somme de Nombres de Fibonacci ou de
Nombres de Lucas. (French)
[Representation of the natural numbers
by a sum of Fibonacci or Lucas numbers] 179--182
Daniel S. Hirschberg A Class of Dynamic Memory Allocation
Algorithms . . . . . . . . . . . . . . . 615--618
K. J. Overholt Efficiency of the Fibonacci Search
Method . . . . . . . . . . . . . . . . . 92--96
A. G. Shannon and
A. F. Horadam Mathematical Notes: Generalized
Fibonacci Number Triples . . . . . . . . 187--190
J. P. R. Tootill and
W. D. Robinson and
D. J. Eagle An Asymptotically Random Tausworthe
Sequence . . . . . . . . . . . . . . . . 469--481
Silvio Maracchia La regola ``Elchatayn'' in Leonardo
Pisano. (Italian) [The Elchatayn rule in
Leonardo Pisano] . . . . . . . . . . . . 321--329
John Brillhart and
D. H. Lehmer and
J. L. Selfridge New primality criteria and
factorizations of $ 2^m \pm 1 $ . . . . 620--647
C. M. Campbell and
E. F. Robertson A note on Fibonacci type groups . . . . 173--176
Ben Cranston and
Rick Thomas Simplified Recombination Scheme for the
Fibonacci Buddy System . . . . . . . . . 331--332
A. F. Horadam Eight hundred years young . . . . . . . 123--134
J. C. P. Miller On Factorisation, with a Suggested New
Approach . . . . . . . . . . . . . . . . 155--172
Michael A. Morrison A Note on Primality Testing Using Lucas
Sequences . . . . . . . . . . . . . . . 181--182
B. R. Myers Spanning Trees, Weighted Compositions,
Fibonacci Numbers, and Resistor Networks 465--474
Stanislaw Glushkov On approximation methods of Leonardo
Fibonacci . . . . . . . . . . . . . . . 291--296
H. C. Williams and
J. S. Judd Determination of the primality of $N$ by
using factors of $ N^2 \pm 1 $ . . . . . 157--172
James L. Peterson and
Theodore A. Norman Buddy Systems . . . . . . . . . . . . . 421--431
I. G. Ba\vsmakova The \booktitleLiber quadratorum of
Leonardo of Pisa. (Russian) . . . . . . 27--37
Judithlynne Carson Fibonacci Numbers and Pineapple
Phyllotaxy . . . . . . . . . . . . . . . 132--136
A. Eswarathasan On square pseudo-Lucas numbers . . . . . 297--304
David W. Roberts The origin of Fibonacci phyllotaxis ---
an analysis of Adler's contact pressure
model and Mitchison's expanding apex
model . . . . . . . . . . . . . . . . . 217--233
Joseph Shortt An iterative program to calculate
Fibonacci numbers in $ O(\log n) $
arithmetic operations . . . . . . . . . 299--303
J. Boothroyd Certification of Algorithm 2: Fibonacci
search . . . . . . . . . . . . . . . . . 86--86
R. E. Crandall and
M. A. Penk A Search for Large Twin Prime Pairs . . 383--388
A. Eswarathasan On pseudo-Lucas numbers of the form $ 2
S^2 $ . . . . . . . . . . . . . . . . . 29--34
A. F. Horadam and
R. P. Loh and
A. G. Shannon Divisibility properties of some
Fibonacci-type sequences . . . . . . . . 55--64
Ettore Picutti The \booktitleBook of squares of
Leonardo of Pisa and the problems of
indeterminate analysis in the Palatine
Codex 557 of the National Library in
Florence. Introduction and comments . . 195--339 (1980)
M. C. Pike and
J. Pixner Algorithm 2: Fibonacci search . . . . . 86--86
Robert Baillie and
Samuel S. Wagstaff, Jr. Lucas Pseudoprimes . . . . . . . . . . . 1391--1417
David Gries and
Gary Levin Computing Fibonacci numbers (and
similarly defined functions) in log time 68--69
C. C. Heyde On a Probabilistic Analogue of the
Fibonacci Sequence . . . . . . . . . . . 1079--1082
Alberto Pettorossi Derivation of an $ O(k^2 \, \log n) $
algorithm for computing order-$k$
Fibonacci numbers from the $ O(k^3 \,
\log n) $ matrix multiplication method 172--179
Carl Pomerance and
J. L. Selfridge and
Samuel S. Wagstaff, Jr. The Pseudoprimes to $ 25 \cdot 10^9 $ 1003--1026
Julia Weszely Fibonacci, Leonardo Pisano (c. 1170--c.
1240). (Romanian) . . . . . . . . . . . 124--126
Thomas C. Wilson and
Joseph Shortt An $ O(\log n) $ algorithm for computing
general order-$k$ Fibonacci numbers . . 68--75
Aldo de Luca A combinatorial property of the
Fibonacci words . . . . . . . . . . . . 193--195
C. C. Heyde On Fibonacci (Or Lagged
Bienaymé--Galton--Watson) Branching
Processes . . . . . . . . . . . . . . . 583--591
Nobuo Miura The Algebra in the \booktitleLiber Abaci
of Leonardo Pisano . . . . . . . . . . . 57--65
Ettore Picutti Sui numeri congruo-congruenti di
Leonardo Pisano. (Italian) [Leonardo of
Pisa's congruous-congruent numbers] . . 141--170
Massimo Bruschi and
Paolo Emilio Ricci An Explicit Formula for $ f(\mathcal
{A}) $ and the Generating Functions of
the Generalized Lucas Polynomials . . . 162--165
Poh Ken Chong The life and work of Leonardo of Pisa 60--66
M. D. McIlroy The Number of States of a Dynamic
Storage Allocation System . . . . . . . 388--392
H. C. Williams A note on the Fibonacci quotient $ F_{p
- \varepsilon } / p $ . . . . . . . . . 366--370
Neyamat Zaheer On Lucas-sets for vector-valued abstract
polynomials in $K$-inner product spaces 832--852
John Brillhart Letter to the editor: ``Properties of
polynomials having Fibonacci numbers for
coefficients'' [Fibonacci Quart. \bf 21
(1983), no. 1, 62--64; MR 84f:10018a] by
D. H. Lehmer and E. Lehmer . . . . . . . 259
M. C. Er Computing Sums of Order-$k$ Fibonacci
Numbers in Log Time . . . . . . . . . . 1--5
M. C. Er Fast Algorithm for Computing Order-$K$
Fibonacci Numbers . . . . . . . . . . . 224--227
Ettore Picutti Il \booktitleFlos di Leonardo Pisano dal
codice E.75.P. sup. della Biblioteca
Ambrosiana di Milano. (Italian) [The
``\booktitleFlos'' of Leonardo Pisano
(from the Codex E.75.P. sup. of the
Ambrosia Library of Milan)] . . . . . . 293--387
Ettore Picutti The ``Flos'' of Leonardo Pisano (dal
codice E. 75 P. sup. della Biblioteca
Ambrosiana di Milano) . . . . . . . . . 293--387
Helmut Prodinger Ordered Fibonacci partitions . . . . . . 312--316
M. R. Williams From Napier to Lucas: The Use of
Napier's Bones in Calculating
Instruments . . . . . . . . . . . . . . 279--296
Curtis Cooper Application of a Generalized Fibonacci
Sequence . . . . . . . . . . . . . . . . 145--147
A. S. Fraenkel Wythoff games, continued fractions,
cedar trees and Fibonacci searches . . . 49--73
Donald E. Knuth and
Erwin Tomash and
M. R. Williams Comments, Queries, and Debate: FORTRAN
implementations; The Madrid promptuary;
Edouard Lucas Vindicated; Photo Essays 402--405
Alain J. Martin and
Martin Rem A presentation of the Fibonacci
algorithm . . . . . . . . . . . . . . . 67--68
Thomas Ottmann and
Arnold L. Rosenberg and
Hans-Werner Six and
Derick Wood Binary search trees with binary
comparison cost . . . . . . . . . . . . 77--101
G. M. Phillips Aitken Sequences and Fibonacci Numbers 354--357
Leonard Curchin and
Roger Herz-Fischler De quand date le premier rapprochement
entre la suite de Fibonacci et la
division en extreme et moyenne raison?.
(French) [When was the first
reconciliation between the Fibonacci
series and division in extreme and mean
reason?] . . . . . . . . . . . . . . . . 129--138
Sherif El-Basil and
Pavel K\vrivka and
Nenad Trinajsti\'c Fibonacci graphs possessing identical
matching polynomials . . . . . . . . . . 2396--2398
R. Franci and
L. Toti Rigatelli Towards a history of algebra from
Leonardo of Pisa to Luca Pacioli . . . . 17--82
George Marsaglia and
Liang-Huei Tsay Matrices and the structure of random
number sequences . . . . . . . . . . . . 147--156
J. H. McCabe and
G. M. Phillips Aitken sequences and generalized
Fibonacci numbers . . . . . . . . . . . 553--558
Parmanand Singh The so-called Fibonacci numbers in
Ancient and Medieval India . . . . . . . 229--244
C. Brezinski and
A. Lembarki Acceleration of extended Fibonacci
sequences . . . . . . . . . . . . . . . 1--8
Benny Chor and
Charles E. Leiserson and
Ronald L. Rivest and
James B. Shearer An Application of Number Theory to the
Organization of Raster-Graphics Memory 86--104
Jean Coquet and
Pascal Van Den Bosch A summation formula involving Fibonacci
digits . . . . . . . . . . . . . . . . . 139--146
C. Taillie and
G. P. Patil The Fibonacci distribution revisited . . 951--959
J. F. Watson Recursion: a choice between readability
and execution speed . . . . . . . . . . 82--90
Alberto Apostolico and
A. S. Fraenkel Robust Transmission of Unbounded Strings
Using Fibonacci Representations . . . . 238--245
John Atkins and
Robert Geist Fibonacci Numbers and Computer
Algorithms . . . . . . . . . . . . . . . 328--336
M. D. Atkinson and
H. W. Chang Computing the number of mergings with
constraints . . . . . . . . . . . . . . 289--292
B. Chazelle and
D. P. Dobkin Intersection of Convex Objects in Two
and Three Dimensions . . . . . . . . . . 1--27
Bruce Jay Collings Compound Random Number Generators . . . 525--527
Michael Cox An alternative approach to recursive
Fibonacci sequences . . . . . . . . . . 38--40
Sherif El-Basil On color polynomials of Fibonacci graphs 956--959
Michael L. Fredman and
Robert Endre Tarjan Fibonacci Heaps and Their Uses in
Improved Network Optimization Algorithms 596--615
David Gries and
Adriano Pascoletti and
Luigi Sbriz Horner's rule and the computation of
linear recurrences . . . . . . . . . . . 237--240
K. Indermark and
H. Klaeren Compiling Fibonacci-like recursion . . . 101--108
Seiichi Nishihara and
Hiroji Nishino Binary Search Revisited: Another
Advantage of Fibonacci Search . . . . . 1132--1135
H. C. Williams Effective primality tests for some
integers of the forms $ {A5}^n - 1 $ and
$ {A7}^n - 1 $ . . . . . . . . . . . . . 385--403
N. S. Altman Bit-wise behavior of random number
generators . . . . . . . . . . . . . . . 941--949
Anonymous Table errata: \em The book of squares
[Academic Press, Boston, Mass., 1987, MR
88m:01021a] by L. P. Fibonacci . . . . . 654--654
John Brillhart and
Peter L. Montgomery and
Robert D. Silverman Supplement to Tables of Fibonacci and
Lucas Factorizations . . . . . . . . . . S1--S15
John Brillhart and
Peter L. Montgomery and
Robert D. Silverman Tables of Fibonacci and Lucas
Factorizations . . . . . . . . . . . . . 251--260, S1--S15
Mike Carlton and
Peter Van Roy Distributed Prolog System with and
Parallelism . . . . . . . . . . . . . . 43--51
James R. Driscoll and
Harold N. Gabow and
Ruth Shrairman and
Robert E. Tarjan Relaxed Heaps: An Alternative to
Fibonacci Heaps with Applications to
Parallel Computation . . . . . . . . . . 1343--1354
S. El-Basil Theory and computational applications of
Fibonacci graphs . . . . . . . . . . . . 1--29
P. Erd\Hos and
P. Kiss and
A. Sárközy A Lower Bound for the Counting Function
of Lucas Pseudoprimes . . . . . . . . . 315--323
Donald E. Knuth Fibonacci multiplication . . . . . . . . 57--60
R. A. MacLeod Generalization of a result of E. Lucas 95--98
Michael I. Rosen Notes: a Proof of the Lucas--Lehmer Test 855--856
J. Shallit A generalization of automatic sequences 1--16
Craig A. Tracy Universality class of a Fibonacci Ising
model . . . . . . . . . . . . . . . . . 481--490
Eric A. Weiss Biographies: Oh, Pioneers! . . . . . . . 348--361
Renato Capocelli Comments and Additions to `Robust
Transmission of Unbounded Strings Using
Fibonacci Representations' . . . . . . . 191--193
Kuo Liang Chung and
Wen Chin Chen and
Ferng-Ching Lin Fast computation of periodic continued
fractions . . . . . . . . . . . . . . . 67--72
Paul Cull and
James L. Holloway Computing Fibonacci numbers quickly . . 143--149
Sherif El-Basil and
Douglas J. Klein Fibonacci numbers in the topological
theory of benzenoid hydrocarbons and
related graphs . . . . . . . . . . . . . 1--23
H. Everett and
A. Gupta Acyclic directed hypercubes may have
exponential diameter . . . . . . . . . . 243--245
C. T. Gray Book Review: \booktitleApplications of
Fibonacci Numbers, by A. N. Philippou;
A. F. Horadam; G. E. Bergum . . . . . . 308--308
Sanjiv Kapoor and
Edward M. Reingold Optimum Lopsided Binary Trees . . . . . 573--590
Jens L. Mennicke On Fibonacci groups and some other
groups . . . . . . . . . . . . . . . . . 117--123
Marco Protasi and
Maurizio Talamo On the number of arithmetical operations
for finding Fibonacci numbers . . . . . 119--124
András Sütö Singular continuous spectrum on a Cantor
set of zero Lebesgue measure for the
Fibonacci Hamiltonian . . . . . . . . . 525--531
Ilias Mihail Vardavas A Fibonacci search technique for model
parameter selection . . . . . . . . . . 65--81
Stuart L. Anderson Random Number Generators on Vector
Supercomputers and Other Advanced
Architectures . . . . . . . . . . . . . 221--251
Margherita Bartolozzi and
Raffaella Franci The theory of proportions in abacus
mathematics from Leonardo Pisano to Luca
Pacioli . . . . . . . . . . . . . . . . 3--28
Richard C. Bollinger and
Charles L. Burchard Lucas's Theorem and Some Related Results
for Extended Pascal Triangles . . . . . 198--204
William F. Eddy Random number generators for parallel
processors . . . . . . . . . . . . . . . 63--71
M. J. Jamieson Notes: Fibonacci Numbers and Aitken
Sequences Revisited . . . . . . . . . . 829--831
Donald E. Knuth A Fibonacci-like sequence of composite
numbers . . . . . . . . . . . . . . . . 21--25
George Marsaglia and
B. Narasimhan and
Arif Zaman A random number generator for PC's . . . 345--349
George Marsaglia and
Arif Zaman and
Wai Wan Tsang Toward a universal random number
generator . . . . . . . . . . . . . . . 35--39
T. Matsui Object-oriented implementation of
EusLisp . . . . . . . . . . . . . . . . 18--40
Ke Qiu and
Henk Meijer A note on diameter of acyclic directed
hypercubes . . . . . . . . . . . . . . . 51--52
Vivek Sarkar Instruction reordering for fork-join
parallelism . . . . . . . . . . . . . . 322--336
Victor J. Duvanenko Efficiently raising matrices to an
integer power . . . . . . . . . . . . . 86--87, 157
Colin Goodall Eigenshape Analysis of a Cut-Grow
Mapping for Triangles, and its
Application to Phyllotaxis in Plants . . 775--798
Daniel M. Gordon and
Carl Pomerance The distribution of Lucas and elliptic
pseudoprimes . . . . . . . . . . . . . . 825--838
B. Iochum and
D. Testard Power law growth for the resistance in
the Fibonacci model . . . . . . . . . . 715--723
H. Lüneburg Fibonaccis aufsteigende Kettenbrüche, ein
elegantes Werkzeug mittelalterlicher
Rechenkunst. (German) [Fibonacci's
ascending continued fractions, an
elegant tool of medieval arithmetic] . . 129--139
Roman E. Maeder The Mathematica Programmer: Fibonacci on
the Fast Track . . . . . . . . . . . . . ??
George Marsaglia and
Arif Zaman A new class of random number generators 462--480
Ivars Peterson Numbers at Random: Number theory
supplies a superior random-number
generator . . . . . . . . . . . . . . . 300--301
Stefan Ronn On the logarithmic evaluation of
recurrence relations . . . . . . . . . . 197--199
P. Seebold Fibonacci morphisms and Sturmian words 365--384
Alberto Cavicchioli and
Fulvia Spaggiari The classification of $3$-manifolds with
spines related to Fibonacci groups . . . 50--78
Elmer K. Hayashi Fibonacci Numbers, Recursion,
Complexity, and Induction Proofs . . . . 407--410
Wen-Jing Hsu and
C. V. Page Embedding mesh in a large family of
graphs . . . . . . . . . . . . . . . . . 149--155
Roman E. Maeder The Mathematica Programmer: Fibonacci on
the Fast Track . . . . . . . . . . . . . ??
Richard J. McIntosh A Generalization of a Congruential
Property of Lucas . . . . . . . . . . . 231--238
Clifford Reiter Fast Fibonacci Numbers . . . . . . . . . ??
Charles Safran The Fibonacci Numbers . . . . . . . . . 43--46
Peter C. Wollan A portable random number generator for
parallel computers . . . . . . . . . . . 1247--1254
Anonymous Sixth International Conference on
Fibonacci Numbers and Their Applications N9
J. W. Bruce A Really Trivial Proof of the
Lucas--Lehmer Test . . . . . . . . . . . 370--371
M. Drmota On Linear Diophantine Equations and
Fibonacci Numbers . . . . . . . . . . . 315--327
Arthur S. Goldstein and
Edward M. Reingold A Fibonacci Version of Kraft's
Inequality Applied to Discrete Unimodal
Search . . . . . . . . . . . . . . . . . 751--777
I. J. Good C399. Trigonometrical factorization of
the Fibonacci and Lucas numbers, and
sums of powers of cotangents . . . . . . 94--99
Daniel M. Gordon and
Carl Pomerance Corrigendum: ``The distribution of Lucas
Pomerance and elliptic pseudoprimes''
[Math. Comp. \bf 57 (1991), no. 196,
825--838, MR 92h:11081] . . . . . . . . 877--877
Wen-Jing Hsu Fibonacci Cubes: a new interconnection
topology . . . . . . . . . . . . . . . . 3--12
R. Lidl and
W. B. Muller Primality testing with Lucas functions 539
George Marsaglia and
Arif Zaman Monkey Tests for Random Number
Generators . . . . . . . . . . . . . . . 1--10
Joseph B. Muskat Generalized Fibonacci and Lucas
sequences and rootfinding methods . . . 365--372
Paolo Emilio Ricci Sum rules for zeros of polynomials and
generalized Lucas polynomials . . . . . 4884--4891
Peter Smith LUC Public-key Encryption: a Secure
Alternative to RSA . . . . . . . . . . . 44, 46, 48--49, 90--92
Kozo Sugiyama Drawing compound digraphs and its
application to an idea organizer
(abstract) . . . . . . . . . . . . . . . 58
V. N. Temlyakov Universality of the Fibonacci cubature
formulas . . . . . . . . . . . . . . . . 178--184
Shu Tezuka and
Masanori Fushimi Calculation of Fibonacci polynomials for
GFSR sequences with low discrepancies 763--770
Shu Tezuka and
Pierre L'Ecuyer and
Raymond Couture On the lattice structure of the
add-with-carry and subtract-with-borrow
random number generators . . . . . . . . 315--331
I. Vattulainen and
K. Kankaala and
J. Saarinen and
T. Ala-Nissila Influence of Implementation on the
Properties of Pseudorandom Number
Generators with a Carry Bit . . . . . . ??
D. Abuaiadh and
J. H. Kingston Are Fibonacci Heaps Optimal? . . . . . . 442
Richard P. Brent On the periods of generalized Fibonacci
recurrences . . . . . . . . . . . . . . 389--401
Aldo de Luca and
Filippo Mignosi Some combinatorial properties of
Sturmian words . . . . . . . . . . . . . 361--385
I. J. Good C416. Fibonacci and Lucas numbers and
trigonometry . . . . . . . . . . . . . . 237--237
Russell Jay Hendel Approaches to the Formula for the $n$ th
Fibonacci Number . . . . . . . . . . . . 139--142
Kazumoto Iguchi A class of new invariant surfaces under
the trace maps for $n$ ary Fibonacci
lattices . . . . . . . . . . . . . . . . 1008--1019
Peter Kirrinnis An optimal bound for path weights in
Huffman trees . . . . . . . . . . . . . 107--110
Pierre L'Ecuyer Uniform random number generation . . . . 77--120
Jun Makino Lagged-Fibonacci random number
generators on parallel computers . . . . 1357--1367
Harald Niederreiter and
Ian H. Sloan Integration of nonperiodic functions of
two variables by Fibonacci lattice rules 57--70
W. P. Petersen Lagged Fibonacci Series Random Number
Generators for the NEC SX-3 . . . . . . 387
Siegfried Schmerling Book Review: \booktitleApplications of
Fibonacci numbers --- volume 5: G. E.
Bergum, A. N. Philippou, A. F. Horadam,
eds. (1993): Dordrecht, Boston, London:
Kluwer Academic Publishers, xxxiv + 625
p., 35 Fig., 30 Tab., ISBN 0-7923-2491-9 603
Peter Smith Cryptography without exponentiation . . 26, 28, 30
Tom R. Swan Algorithm Alley . . . . . . . . . . . . 111
Antonio Albano and
Giorgio Ghelli and
Renzo Orsini Fibonacci: a Programming Language for
Object Databases . . . . . . . . . . . . 403--444
R. Anderson On Fibonacci keystream generators . . . 346
A. V. Anisimov Linear Fibonacci Forms and Parallel
Algorithms for High Dimension Arithmetic 16
Anonymous Fibonacci Forgeries . . . . . . . . . . 82
Anonymous Mathematical Recreations . . . . . . . . 96
François Arnault Constructing Carmichael Numbers Which
are Strong Pseudoprimes to Several Bases 151--162 (or 151--161??)
Daniel Bleichenbacher and
Wieb Bosma and
Arjen K. Lenstra Some Remarks on Lucas-Based
Cryptosystems . . . . . . . . . . . . . 386--396
Aldo de Luca A division property of the Fibonacci
word . . . . . . . . . . . . . . . . . . 307--312
Xavier Droubay Palindromes in the Fibonacci word . . . 217--221
Jürgen Eichenauer-Herrmann Pseudorandom Number Generation by
Nonlinear Methods . . . . . . . . . . . 247--255
Derek F. Holt An alternative proof that the Fibonacci
group $ F(2, 9) $ is infinite . . . . . 97--100
Chi Sung Laih and
Fu Kuan Tu and
Wen Chung Tai On the security of the Lucas function 243--247
Óscar Martín-Sánchez and
Cristóbal Pareja-Flores A gentle introduction to algorithm
complexity for CS1 with nine variations
on a theme by Fibonacci . . . . . . . . 49--56
Michael Mascagni and
Steven A. Cuccaro and
Daniel V. Pryor and
M. L. Robinson A Fast, High Quality, and Reproducible
Parallel Lagged-Fibonacci Pseudorandom
Number Generator . . . . . . . . . . . . 211--219
Pontus Matstoms Parallel sparse $ Q R $ factorization on
shared memory architectures . . . . . . 473--486
H. R. Morton Fibonacci-like sequences and greatest
common divisors . . . . . . . . . . . . 731--734
Ora E. Percus and
Paula A. Whitlock Theory and application of Marsaglia's
monkey test for pseudorandom number
generators . . . . . . . . . . . . . . . 87--100
David L. Ranum On some applications of Fibonacci
numbers . . . . . . . . . . . . . . . . 640--645
P. Smith and
C. Skinner A public-key cryptosystem and a digital
signature system based on the Lucas
function analogue to discrete logarithms 357
P. Smith and
C. Skinner A public-key cryptosystem and a digital
signature system based on the Lucas
function analogue to discrete logarithms 357
Ian Stewart Mathematical Recreations: Fibonacci
Forgeries . . . . . . . . . . . . . . . 102--105
Paul M. Voutier Primitive divisors of Lucas and Lehmer
sequences . . . . . . . . . . . . . . . 869--888
Adam Webber Optimization of Functional Programs by
Grammar Thinning . . . . . . . . . . . . 293--330
S. Y. Yan Primality testing of large numbers in
Maple . . . . . . . . . . . . . . . . . 1--8
Valérie Berthé Frequences des facteurs des suites
sturmiennes. (French) [Frequencies of
factors of Sturmian series] . . . . . . 295--309
Peter Kok Keong Loh and
Wen Jing Hsu and
Cai Wentong and
Nadarajah Sriskanthan How Network Topology Affects Dynamic
Load Balancing . . . . . . . . . . . . . 25--35
Wojciech Plandowski and
Wojciech Rytter and
Tomasz Szymacha Parallel tree-contraction and Fibonacci
numbers . . . . . . . . . . . . . . . . 267--271
Haifeng Qian and
Jie Wu Enhanced Fibonacci Cubes . . . . . . . . 331--345
Milan Randi\'c and
Daniel A. Morales and
Oswaldo Araujo Higher-order Fibonacci numbers . . . . . 79--94
Jack Ryder Exploring Fibonacci Numbers Mod $M$ . . 122--124
Luca Trevisan A note on minimum-area upward drawing of
complete and Fibonacci trees . . . . . . 231--236
L. Trevisan A note on minimum-area upward drawing of
complete and Fibonacci trees . . . . . . 231
Doron Zeilberger Self-avoiding walks, the language of
science, and Fibonacci numbers . . . . . 135--138
Srinivas Aluru Lagged Fibonacci Random Number
Generators for Distributed Memory
Parallel Computers . . . . . . . . . . . 1--12
F. Arnault The Rabin--Monier theorem for Lucas
pseudoprimes . . . . . . . . . . . . . . 869--881
John Boyer Algorithm Alley --- Heaps are usually
implemented via binary trees, with the
property that for every subtree, the
root is the minimum item. Here, John
describes how to implement exceptionally
fast `Fibonacci' heaps . . . . . . . . . 106
Aldo de Luca Standard Sturmian morphisms . . . . . . 205--224
Dale K. Hathaway and
Stephen L. Brown Fibonacci Powers and a Fascinating
Triangle . . . . . . . . . . . . . . . . 124--128
Wen-Jing Hsu and
Moon Jung Chung and
Amitabha Das Linear Recursive Networks and Their
Applications in Distributed Systems . . 673--680
Costas S. Iliopoulos and
Dennis Moore and
W. F. Smyth A characterization of the squares in a
Fibonacci string . . . . . . . . . . . . 281--291
Bob Jenkins Algorithm Alley: Hash Functions . . . . 107--109, 115--116
Feng-Shr Jiang and
Shi-Jinn Horng and
Tzong-Wann Kao Embedding of Generalized Fibonacci Cubes
in Hypercubes with Faulty Nodes . . . . 727--737
Marc Joye and
Jean-Jacques Quisquater Protocol Failures for RSA-Like Functions
Using Lucas Sequences and Elliptic
Curves . . . . . . . . . . . . . . . . . 93--100
G.-Y. Lee and
S.-G. Lee and
H.-G. Shin On the $K$-Generalized Fibonacci Matrix
$ Q^*_k $ . . . . . . . . . . . . . . . 73--88
Peter K. K. Loh and
Hsu Wen Jing Dynamic load balancing on multiprocessor
networks . . . . . . . . . . . . . . . . 369--372
Jayanta Sarkar and
Manas Banerjee and
Asok K. Mukherjee Lucas Sequences and Fibonacci Triads of
Graphs in PMO Calculation on the
Charge-Transfer Bands of a Series of EDA
Complexes: Correlation with Experimental
and AM1 Results . . . . . . . . . . . . 817--825
Jie Wu Extended Fibonacci Cubes . . . . . . . . 1203--1210
John Boyer Algorithm Alley: Resizable Data
Structures . . . . . . . . . . . . . . . 115--116, 118, 129
Erik Jensen and
Ronald Rusay Musical Representations of the Fibonacci
String and Proteins . . . . . . . . . . ??
M. T. Rivolo and
A. Simi Il Calcolo delle Radici Quadrate e
Cubiche in Italia da Fibonacci a
Bombelli. (Italian) [The calculation of
square and cube roots in Italy from
Fibonacci to Bombelli] . . . . . . . . . 161--193
Patrice Séébold On the conjugation of standard morphisms 91--109
Arthur T. Benjamin and
Jennifer J. Quinn Recounting Fibonacci and Lucas
Identities . . . . . . . . . . . . . . . 359--366
Robert L. Devaney The Mandelbrot set, the Farey tree, and
the Fibonacci sequence . . . . . . . . . 289--302
Harvey Dubner and
Wilfrid Keller New Fibonacci and Lucas primes . . . . . 417--427
Mark Embree and
Lloyd N. Trefethen Growth and decay of random Fibonacci
sequences . . . . . . . . . . . . . . . 2471--2485
Aviezri S. Fraenkel and
Jamie Simpson The exact number of squares in Fibonacci
words . . . . . . . . . . . . . . . . . 95--106
Ivars Peterson Fibonacci at Random: Uncovering a new
mathematical constant . . . . . . . . . 376--377
John S. Robertson How many recursive calls does a
recursive function make? . . . . . . . . 60--61
V. Scarano On the Sizes of Extended Fibonacci Cubes 764
Ching-Te Wang and
Chin-Chen Chang and
Chu-Hsing Lin A method for computing Lucas sequences 187--196
Jin Tao Xiong and
Hong Xiu Liu and
De Zhong Pi The Lucas public-key cryptosystem and
its security . . . . . . . . . . . . . . 397--401
Alberto Apostolico and
Valentin E. Brimkov Fibonacci arrays and their
two-dimensional repetitions . . . . . . 263--273
Gwang-Yeon Lee $k$-Lucas numbers and associated
bipartite graphs . . . . . . . . . . . . 51--61
Michael Mascagni and
Ashok Srinivasan Algorithm 806: SPRNG: a scalable library
for pseudorandom number generation . . . 436--461
Michael Mascagni and
Ashok Srinivasan Corrigendum: Algorithm 806: SPRNG: a
scalable library for pseudorandom number
generation . . . . . . . . . . . . . . . 618--619
Amos O. Olagunju The role of scientific discovery in
teaching and learning of computer
science . . . . . . . . . . . . . . . . 28--31
Maryvonne Spiesser Probl\`emes linéaires dans le
\booktitleCompendy de la praticque des
nombres de Barthélemy de Romans et
Mathieu Préhoude (1471): une approche
nouvelle basée sur des sources proches du
\booktitleLiber abbaci de Léonard de
Pise. (French) [Linear problems in the
\booktitleCompendium of the number
practice by Barthélemy de Romans and
Mathieu Préhoude (1471): an new approach
based on sources near \booktitleLiber
abbaci of Leonardo of Pisa] . . . . . . 362--383
Maryvonne Spiesser Probl\`emes linéaires dans le
\booktitleCompendy de la praticque des
nombres de Barthélemy de Romans et
Mathieu Préhoude (1471): une approche
nouvelle basée sur des sources proches du
\booktitleLiber abbaci de Léonard de
Pise. (French) [Linear problems in the
\booktitleCompendium of the number
practice by Barthélemy de Romans and
Mathieu Préhoude (1471): an new approach
based on sources near \booktitleLiber
abbaci of Leonardo of Pisa] . . . . . . 362--383
Grzegorz Stachowiak Fibonacci Correction Networks . . . . . 535
Daisuke Takahashi A fast algorithm for computing large
Fibonacci numbers . . . . . . . . . . . 243--246
Divakar Viswanath Random Fibonacci sequences and the
number $ 1.13198824 \dots $ . . . . . . 1131--1155
Guo-Jun Wang Separable Boolean functions and
generalized Fibonacci sequences . . . . 205--216
Franco Eugeni and
Raffaele Mascella A note on generalized Fibonacci numbers 33--45
Peter J. Ferraro Fibonacci Numbers and Powers: 10765 . . 978--979
A. Shum and
P. M. Melliar-Smith and
L. E. Moser Design and evaluation of the Fibonacci
optical ATM switch . . . . . . . . . . . 466--481
Nathan D. Cahill and
John R. D'Errico and
Darren A. Narayan and
Jack Y. Narayan Fibonacci Determinants . . . . . . . . . 221--225
Raffaella Franci The \booktitleLiber abaci of Leonardo
Fibonacci, 1202--2002 . . . . . . . . . 293--328
David Ginat Aha! an illuminating perspective . . . . 1--2
M. J. Jamieson Fibonacci Numbers and Cotangent
Sequences . . . . . . . . . . . . . . . 655--657
Gokul B. Kandiraju and
Anand Sivasubramaniam Characterizing the $d$-TLB behavior of
SPEC CPU2000 benchmarks . . . . . . . . 129--139
Martin Kutz Lower Bounds for Lucas Chains . . . . . 1896--1908
Nick MacKinnon and
Stephen M. Gagola, Jr. Fibonacci Twin Primes: 10844 . . . . . . 78--78
George Marsaglia and
Wai Wan Tsang Some Difficult-to-Pass Tests of
Randomness . . . . . . . . . . . . . . . 1--8
Carl Miller and
Donald E. Knuth A Fibonacci--Lucas Extremum: 10825 . . . 762--763
Nobuo Miura Leonardo of Pisa and cubic equations . . 37--47
Corinna Rossi and
Christopher A. Tout Were the Fibonacci Series and the Golden
Section Known in Ancient Egypt? . . . . 101--113
Djamil Aissani and
Dominique Valerian Mathématiques, commerce et société \`a
Béja\"\ia (Bugia) au moment du séjour de
Leonardo Fibonacci XII$^{\rm
e}$--XIII$^{\rm e}$ si\`ecles . . . . . 9--31 (2005)
Kevin A. Broughan Adic Topologies for the Rational
Integers . . . . . . . . . . . . . . . . 711--723
Enrique Canessa Theory of Analogous Force on Number Sets
Enrique Canessa Theory of analogous force on number sets 44--52
Ramazan Dikici and
Engin Özkan An application of Fibonacci sequences in
groups . . . . . . . . . . . . . . . . . 323--331
Raffaella Franci Leonardo Fibonacci and treatises on the
abacus in Italy in the fourteenth and
fifteenth centuries . . . . . . . . . . 33--54 (2005)
Erdal Karaduman and
Hüseyin Aydìn General $2$-step Fibonacci sequences in
nilpotent groups of exponent $p$ and
nilpotency class $4$ . . . . . . . . . . 491--497
Erdal Karaduman and
U\ugur Yavuz On the period of Fibonacci sequences in
nilpotent groups . . . . . . . . . . . . 321--332
Gwang-Yeon Lee and
Jin-Soo Kim The linear algebra of the $k$-Fibonacci
matrix . . . . . . . . . . . . . . . . . 75--87
M. Margenstern and
G. Skordev Fibonacci Type Coding for the Regular
Rectangular Tilings of the Hyperbolic
Plane . . . . . . . . . . . . . . . . . 398--422
Michael Mitzenmacher A Brief History of Generative Models for
Power Law and Lognormal Distributions 226--251
Engin Özkan and
Hüseyin Aydìn and
Ramazan Dikici Applications of Fibonacci sequences in a
finite nilpotent group . . . . . . . . . 565--578
Engin Özkan and
Hüseyin Aydìn and
Ramazan Dikici $3$-Step Fibonacci series modulo $m$ . . 165--172
Engin Özkan $3$-Step Fibonacci sequences in
nilpotent groups . . . . . . . . . . . . 517--527
Luigi Pepe Leonardo Fibonacci in the eighteenth
century . . . . . . . . . . . . . . . . 75--86 (2005)
Timothy J. Rolfe Spreadsheet-aided numerical
experimentation: analytic formula for
Fibonacci numbers . . . . . . . . . . . 117--119
Rajae Ben Taher and
Mustapha Rachidi On the matrix powers and exponential by
the $r$-generalized Fibonacci sequences
methods: the companion matrix case . . . 341--353
Bünyamin Yildiz and
Erdal Karaduman On Fibonacci search method with
$k$-Lucas numbers . . . . . . . . . . . 523--531
Anonymous Errata for 2004: Fibonacci in Complex
Camouflage: 10858 . . . . . . . . . . . 922--922
J. T. Astola and
K. Egiazarian and
M. Stankovi\'c and
R. S. Stankovi\'c Fibonacci Arithmetic Expressions . . . . 842--856
Pedro Berrizbeitia and
T. G. Berry Biquadratic reciprocity and a Lucasian
primality test . . . . . . . . . . . . . 1559--1564
Marcia Edson and
Luca Q. Zamboni On representations of positive integers
in the Fibonacci base . . . . . . . . . 241--260
Menso Folkerts Leonardo Fibonacci's knowledge of
Euclid's \booktitleElements and of other
mathematical texts . . . . . . . . . . . 93--113 (2005)
L. F. Johnson Tumble, a fast simple iteration
algorithm for Fibonacci . . . . . . . . 187--189
Erdal Karaduman An application of Fibonacci numbers in
matrices . . . . . . . . . . . . . . . . 903--908
Donald E. Knuth and
Robin Chapman Fibonacci in Complex Camouflage: 10858 166--167
Michael Mascagni and
Ashok Srinivasan Parameterizing parallel multiplicative
lagged-Fibonacci generators . . . . . . 899--916
Clifford A. Reiter Views of Fibonacci dynamics . . . . . . 297--300
Murat Subasi and
Necmettin Yildirim and
Bünyamin Yildiz An improvement on Fibonacci search
method in optimization theory . . . . . 893--901
Dursun Tasci and
Emrah Kilic On the order-$k$ generalized Lucas
numbers . . . . . . . . . . . . . . . . 637--641
Dov Aharonov and
Alan Beardon and
Kathy Driver Fibonacci, Chebyshev, and Orthogonal
Polynomials . . . . . . . . . . . . . . 612--630
Demetrios L. Antzoulakos and
Markos V. Koutras On a class of polynomials related to
classical orthogonal and Fibonacci
polynomials with probability
applications . . . . . . . . . . . . . . 18--39
Jean-Luc Baril and
Vincent Vajnovszki Minimal change list for Lucas strings
and some graph theoretic consequences 189--199
H. Bruin and
O. Volkova The complexity of Fibonacci-like
kneading sequences . . . . . . . . . . . 379--389
Joseph Callaghan and
John J. Chew III and
Stephen M. Tanny On the Behavior of a Family of
Meta-Fibonacci Sequences . . . . . . . . 794--824
Gyoung-Sik Choi and
Suk-Geun Hwang and
Ik-Pyo Kim and
Bryan L. Shader $ (\pm 1) $-Invariant sequences and
truncated Fibonacci sequences . . . . . 303--312
Wai-Fong Chuan and
Hui-Ling Ho Locating factors of the infinite
Fibonacci word . . . . . . . . . . . . . 429--442
Jens Hòyrup Leonardo Fibonacci and \it Abbaco
culture. A proposal to invert the roles 23--56
Emin Kahya Comment on titled ``On Fibonacci search
method with $k$-Lucas numbers'' . . . . 1321--1324
Erdal Karaduman On determinants of matrices with general
Fibonacci numbers entries . . . . . . . 670--676
Yannis Manolopoulos On the number of recursive calls of
recursive functions . . . . . . . . . . 61--64
Alan C. Newell and
Patrick D. Shipman Plants and Fibonacci . . . . . . . . . . 937--968
Ahmet Ali Öcal and
Naim Tuglu and
Ercan Altini\csik On the representation of $k$-generalized
Fibonacci and Lucas numbers . . . . . . 584--596
Süleyman Solak On the norms of circulant matrices with
the Fibonacci and Lucas numbers . . . . 125--132
Emin Kahya Comment on titled ``An improvement on
Fibonacci search method in optimization
theory'' . . . . . . . . . . . . . . . . 753--756
Eran Makover and
Jeffrey McGowan An elementary proof that random
Fibonacci sequences grow exponentially 40--44
Wojciech Rytter The structure of subword graphs and
suffix trees of Fibonacci words . . . . 211--223
Michael Z. Spivey Fibonacci Identities via the Determinant
Sum Property . . . . . . . . . . . . . . 286--289
R. Ben Taher and
M. Mouline and
Mustapha Rachidi Fibonacci--Horner decomposition of the
matrix exponential and the fundamental
system of solutions . . . . . . . . . . 178--190
Nevine Maurice Ebeid and
M. Anwar Hasan On $ \tau $-adic representations of
integers . . . . . . . . . . . . . . . . 271--296
D. E. Giles Benford's Law and naturally occurring
prices in certain eBay auctions . . . . 157--161
John Hannah False position in Leonardo of Pisa's
\booktitleLiber abbaci . . . . . . . . . 306--332
Emrah Kilic The generalized order-$k$
Fibonacci--Pell sequence by matrix
methods . . . . . . . . . . . . . . . . 133--145
Harris Kwong Two determinants with Fibonacci and
Lucas entries . . . . . . . . . . . . . 568--571
Richard J. McIntosh and
Eric L. Roettger A search for Fibonacci--Wieferich and
Wolstenholme primes . . . . . . . . . . 2087--2094
Manuel Rubio-Sánchez and
Isidoro Hernán-Losada Exploring recursion with Fibonacci
numbers . . . . . . . . . . . . . . . . 359--359
Süleyman Solak Erratum to ``On the norms of circulant
matrices with the Fibonacci and Lucas
numbers'' [Appl. Math. Comput. 160
(2005) 125--132] . . . . . . . . . . . . 1855--1856
Murat Suba\csì Reply to the Comment of E. Kahya on ``An
improvement on Fibonacci search method
in optimization theory'' by Murat
Suba\csì, Necmettin Yildirim, Bünyamin
Yildiz, [An improvement on Fibonacci
search method in optimization theory,
Applied Mathematics and Computation \bf
147 (2004) 893--901] . . . . . . . . . . 1059--1060
Andrej Taranenko and
Aleksander Vesel Fast Recognition of Fibonacci Cubes . . 81--93
K. Uslu and
A. Nalli and
M. Sen Erratum to ``On the norms of circulant
matrices with the Fibonacci and Lucas
numbers'' [Appl. Math. Comput. 160 (1)
(2005) 125--132] . . . . . . . . . . . . 997--998
Jonathan Bayless The Lucas--Pratt primality tree . . . . 495--502
Ezra Brown and
Jason C. Brunson Fibonacci's Forgotten Number . . . . . . 112--120
Jens Christian Claussen Time evolution of the rule $ 150 $
cellular automaton activity from a
Fibonacci iteration . . . . . . . . . . 062701
Ali Demir and
Nese Omur and
Yucel Turker Ulutas Optimization by $k$-Lucas numbers . . . 366--371
Ali Demir and
Nese Omur and
Yucel Turker Ulutas Parametrized Fibonacci search method
with $k$-Lucas numbers . . . . . . . . . 355--360
Ali Demir Trisection method by $k$-Lucas numbers 339--345
Ayhan Dil and
István Mez\Ho A symmetric algorithm for hyperharmonic
and Fibonacci numbers . . . . . . . . . 942--951
E. Foundas and
Ch. Lytras and
C. Patsakis Improved algorithms for the calculation
of Fibonacci numbers . . . . . . . . . . 113--120
E. Foundas and
C. Patsakis and
G. Chondrocoukis Lucas permutations and some notes on
Fibonacci permutations . . . . . . . . . 181--190
Xu Dan Fu and
Xia Zhou and
Xiao Dong Zhao Extensions of Lucas' congruence and
Babbage's congruence . . . . . . . . . . 693--698
Xudan Fu and
Xia Zhou On matrices related with Fibonacci and
Lucas numbers . . . . . . . . . . . . . 96--100
Massimo Galuzzi Book Review: Alfred S. Posamentier and
Ingmar Lehmann, \booktitleThe (Fabulous)
Fibonacci Numbers. New York: Prometheus
Books, 2007. 385 pp., ISBN
976-1-59102-475-0 . . . . . . . . . . . 188--189
Élise Janvresse and
Beno\^\it Rittaud and
Thierry de la Rue How do random Fibonacci sequences grow? 619--648
A. Juarna and
V. Vajnovszki Combinatorial isomorphism between
Fibonacci classes . . . . . . . . . . . 147--158
Haim Kaplan and
Robert Endre Tarjan Thin heaps, thick heaps . . . . . . . . 3:1--3:??
Michael A. Kelsey Dethroning Fibonacci Sequence (abstract
only) . . . . . . . . . . . . . . . . . 78--78
Hee Sik Kim and
J. Neggers Fibonacci mean and golden section mean 228--232
Ali Reza Moghaddamfar and
S. Navid Salehy and
S. Nima Salehy Certain matrices related to the
Fibonacci sequence having recursive
entries . . . . . . . . . . . . . . . . 543--576
Adam Mosley Book Reviews: Stephen Clucas (ed.) John
Dee: Interdisciplinary Studies in
English Renaissance Thought.
International Archives of the History of
Ideas, 193. Dordrecht: Springer, 2006.
Pp. xvii + 366. ISBN: 1-4020-4245-0.
EUR144.00, \$189.00, \pounds 111.00
(hardback). ISBN: 1-4020-4246-9
(e-book)} . . . . . . . . . . . . . . . 132--134
Manuel Rubio-Sánchez An introduction to problem equivalence
with combinatorics . . . . . . . . . . . 313--313
Roberto Tauraso and
O. P. Lossers Fibonacci Numbers and Tilling a Board
with Cuts: 11241 . . . . . . . . . . . . 858--859
Michael Wirth Introducing recursion by parking cars 52--55
Michel E. Beleza Yamagishi and
Alex Itiro Shimabukuro Nucleotide Frequencies in Human Genome
and Fibonacci Numbers . . . . . . . . . 643--653
Sheng-liang Yang On the $k$-generalized Fibonacci numbers
and high-order linear recurrence
relations . . . . . . . . . . . . . . . 850--857
Edward Dunne Long days on the Fibonacci clock . . . . 127--134
Sergio Falcon and
Angel Plaza On $k$-Fibonacci numbers of arithmetic
indexes . . . . . . . . . . . . . . . . 180--185
Kevin Hartshorn Book Review: \booktitleThe fabulous
Fibonacci numbers by Alfred Posamentier
and Ingmar Lehmann . . . . . . . . . . . 113--116
Jens Hòyrup Book Review: \booktitleFibonacci's De
Practica Geometrie, Barnabas Hughes
(Ed.), in: Sources and Studies in the
History of Mathematics and Physical
Sciences. Springer, New York (2008),
ISBN 978-0-387-72930-5 . . . . . . . . . 73--77
E. C. Laskari and
G. C. Meletiou and
M. N. Vrahatis Aitken and Neville inverse interpolation
methods for the Lucas logarithm problem 52--56
Richard Maruszewski Fibonacci's Forgotten Number Revisited 248--251
Jeffrey A. Oaks Reviews: \booktitleFibonacci's
\booktitleDe Practica Geometrie --- by
Barnabas Hughes . . . . . . . . . . . . 168--169
Manjusri Basu and
Bandhu Prasad Long range variations on the Fibonacci
universal code . . . . . . . . . . . . . 1925--1931
Wenchang Chu Fibonacci polynomials and Sylvester
determinant of tridiagonal matrix . . . 1018--1023
Edgardo Cureg and
Arunava Mukherjea Numerical results on some generalized
random Fibonacci sequences . . . . . . . 233--246
Moawwad El-Mikkawy and
Tomohiro Sogabe A new family of $k$-Fibonacci numbers 4456--4461
Mostafa Esmaeili and
Morteza Esmaeili A Fibonacci-polynomial based coding
method with error detection and
correction . . . . . . . . . . . . . . . 2738--2752
Jeong Soon Han and
Hee Sik Kim and
J. Neggers The Fibonacci-Norm of a Positive
Integer: Observations and Conjectures 371--385
Barnabas Hughes An early abridgement of Fibonacci's De
practica geometrie . . . . . . . . . . . 615--640
Élise Janvresse and
Beno\^\it Rittaud and
Thierry de la Rue Almost-sure growth rate of generalized
random Fibonacci sequences . . . . . . . 135--158
Dong-mei Jiang Application of Fibonacci sine and cosine
function to a nonlinear
differential--difference equation . . . 3898--3902
Shmuel T. Klein and
Miri Kopel Ben-Nissan On the Usefulness of Fibonacci
Compression Codes . . . . . . . . . . . 701--716
K. S. Enoch Lee On the Sum of a Prime and a Fibonacci
Number . . . . . . . . . . . . . . . . . 1669--1676
H. Matsui and
D. Minematsu and
T. Yamauchi and
R. Miy Adera Pascal-like triangles and Fibonacci-like
sequences . . . . . . . . . . . . . . . 27--41
Shouqiang Shen and
Jianmiao Cen On the bounds for the norms of
$r$-circulant matrices with the
Fibonacci and Lucas numbers . . . . . . 2891--2897
Bartosz Walczak A simple representation of subwords of
the Fibonacci word . . . . . . . . . . . 956--960
T. Becker and
A. Greaves-Tunnell and
S. J. Miller and
R. Ronan and
F. W. Strauch Benford's Law and Continuous Dependent
Random Variables . . . . . . . . . . . .
Aline Castro and
Sandi Klavzar and
Michel Mollard and
Yoomi Rho On the domination number and the
$2$-packing number of Fibonacci cubes
and Lucas cubes . . . . . . . . . . . . 2655--2660
C. M. da Fonseca Some open questions on the Fibonacci
polytope . . . . . . . . . . . . . . . . 317
Barnaby Dalton and
Mustazee Rahman and
Stephen Tanny Spot-Based Generations for
Meta-Fibonacci Sequences . . . . . . . . 129--137
Jacek Dziok and
Ravinder Krishna Raina and
Janusz Sokól On $ \alpha $-convex functions related
to shell-like functions connected with
Fibonacci numbers . . . . . . . . . . . 996--1002
Jacek Dziok and
Ravinder Krishna Raina and
Janusz Sokól Certain results for a class of convex
functions related to a shell-like curve
connected with Fibonacci numbers . . . . 2605--2613
Jishe Feng Fibonacci identities via the determinant
of tridiagonal matrix . . . . . . . . . 5978--5981
N. Gauthier 95.50 Fractional-power identities for
Fibonacci and Lucas polynomials and
numbers . . . . . . . . . . . . . . . . 486--494
Jeong Soon Han and
Hee Sik Kim and
J. Neggers Acknowledgment of priority: ``The
Fibonacci-norm of a positive integer:
Observations and conjectures'' . . . . . 853--854
John Hannah Conventions for recreational problems in
Fibonacci's \booktitleLiber Abbaci . . . 155--180
Kiyoshi Inoue and
Sigeo Aki Bivariate Fibonacci polynomials of order
$k$ with statistical applications . . . 197--210
Ahmet \.Ipek On the spectral norms of circulant
matrices with classical Fibonacci and
Lucas numbers entries . . . . . . . . . 6011--6012
Yueheng Lan Novel Computation of the Growth Rate of
Generalized Random Fibonacci Sequences 847--861
Florian Luca and
Carl Pomerance and
Stephan Wagner Fibonacci integers . . . . . . . . . . . 440--457
Shi-Mei Ma Identities involving generalized
Fibonacci-type polynomials . . . . . . . 9297--9301
Ognjen Milatovic 95.21 A property of odd terms of a
generalised Fibonacci sequence . . . . . 262--264
Rob F. Remis On the relation between FDTD and
Fibonacci polynomials . . . . . . . . . 1382--1386
Norman Routledge 95.49 Generalised Fibonacci Properties 483--486
Shou-Qiang Shen and
Jian-Miao Cen and
Yong Hao On the determinants and inverses of
circulant matrices with Fibonacci and
Lucas numbers . . . . . . . . . . . . . 9790--9797
Naim Tuglu and
E. Gokcen Kocer and
Alexey Stakhov Bivariate Fibonacci like $p$-polynomials 10239--10246
Elisabetta Ulivi On Leonardo Fibonacci and on masters of
the abacus in Pisa from the thirteenth
to the fifteenth century . . . . . . . . 247--286
Peter Winkler Last Byte: Puzzled: Uncommon Divisors 120--120
Omer Yayenie A note on generalized Fibonacci
sequences . . . . . . . . . . . . . . . 5603--5611
Durmus Bozkurt and
Tin-Yau Tam Determinants and inverses of circulant
matrices with Jacobsthal and
Jacobsthal--Lucas Numbers . . . . . . . 544--551
Hongwei Chen and
Chris Kennedy Harmonic Series Meets Fibonacci Sequence 237--243
Sören Christensen Generalized Fibonacci numbers and
Blackwell's renewal theorem . . . . . . 1665--1668
Wai-Fong Chuan and
Fang-Yi Liao and
Hui-Ling Ho and
Fei Yu Fibonacci word patterns in two-way
infinite Fibonacci words . . . . . . . . 69--81
L. Hajdu and
M. Szikszai On the GCD-s of $k$ consecutive terms of
Lucas sequences . . . . . . . . . . . . 3056--3069
Michael Hanlon Turing's flower theory blossoms . . . .
John Hannah \booktitleThe man of numbers:
Fibonacci's arithmetic revolution [book
review, Walker and Co., New York, NY,
2011] . . . . . . . . . . . . . . . . . 661--664
Charles E. Leiserson and
Tao B. Schardl and
Jim Sukha Deterministic parallel random-number
generation for dynamic-multithreading
platforms . . . . . . . . . . . . . . . 193--204
Hsuan-Chu Li On Fibonacci--Hessenberg matrices and
the Pell and Perrin numbers . . . . . . 8353--8358
J. Petronilho Generalized Fibonacci sequences via
orthogonal polynomials . . . . . . . . . 9819--9824
Ákos Pintér and
Volker Ziegler On arithmetic progressions in
recurrences --- a new characterization
of the Fibonacci sequence . . . . . . . 1686--1706
B. N. B. Ray and
Alok Ranjan Tripathy and
S. P. Mohanty Parallel Hermite Interpolation on
Extended Fibonacci Cubes . . . . . . . . 36--41
Arto Salomaa Subword occurrences, weighted automata
and iterated morphisms, especially the
Fibonacci morphism . . . . . . . . . . . 85--93
Ulrich Seyfarth and
Kedar S. Ranade Cyclic mutually unbiased bases,
Fibonacci polynomials and Wiedemann's
conjecture . . . . . . . . . . . . . . . 062201
Francisco Aragón Artacho and
David H. Bailey and
Jonathan M. Borwein and
Peter B. Borwein Walking on Real Numbers . . . . . . . . 42--60
Jhon J. Bravo and
Florian Luca Corrigendum to ``Coincidences in
generalized Fibonacci sequences'' [J.
Number Theory \bf 133 (6) (2013)
2121--2137] . . . . . . . . . . . . . . 3205--3205
Jhon J. Bravo and
Florian Luca Coincidences in generalized Fibonacci
sequences . . . . . . . . . . . . . . . 2121--2137
Jhon J. Bravo and
Florian Luca On the largest prime factor of the
$k$-Fibonacci numbers . . . . . . . . . 1351--1366
Jin-Yi Cai and
Pinyan Lu and
Mingji Xia Holographic algorithms by Fibonacci
gates . . . . . . . . . . . . . . . . . 690--707
David Damanik and
Paul Munger and
William N. Yessen Orthogonal Polynomials on the Unit
Circle with Fibonacci Verblunsky
Coefficients, II. Applications . . . . . 339--362
A. S. Di Domenico Integer sequences that behave as
Fibonacci--Lucas pairs . . . . . . . . . 1--7
Martin Griffiths From golden-ratio equalities to
Fibonacci and Lucas identities . . . . . 234--241
H. H. Gulec and
N. Taskara and
K. Uslu A new approach to generalized Fibonacci
and Lucas numbers with binomial
coefficients . . . . . . . . . . . . . . 482--486
Kenan Kaygìsìz and
Adem \cSahin A new method to compute the terms of
generalized order-$k$ Fibonacci numbers 3119--3126
Emrah Kiliç and
Talha Arikan More on the infinite sum of reciprocal
Fibonacci, Pell and higher order
recurrences . . . . . . . . . . . . . . 7783--7788
Ay\cse Kurt and
Salih Yalçìnba\cs and
Mehmet Sezer Fibonacci Collocation Method for Solving
Linear Differential--Difference
Equations . . . . . . . . . . . . . . . 448--458
John D. LaGrange A combinatorial development of Fibonacci
numbers in graph spectra . . . . . . . . 4335--4347
R. Marques and
C. Bouville and
M. Ribardi\`ere and
L. P. Santos and
K. Bouatouch Spherical Fibonacci Point Sets for
Illumination Integrals . . . . . . . . . 134--143
Geetanjali Panda and
Suman Ghosh A derivative free multidimensional
optimal search method using Lucas number 6536--6541
Vasileios Porpodas and
Marcelo Cintra LUCAS: latency-adaptive unified cluster
assignment and instruction scheduling 45--54
Salvador Roura Fibonacci BSTs: a new balancing method
for binary search trees . . . . . . . . 48--59
Jawad Sadek and
Russell Euler Divisibility properties for Fibonacci
and related numbers . . . . . . . . . . 461--464
Andrzej Wloch Some identities for the generalized
Fibonacci numbers and the generalized
Lucas numbers . . . . . . . . . . . . . 5564--5568
Goksal Bilgici Two generalizations of Lucas sequence 526--538
Karel B\vrinda and
Edita Pelantová and
Ond\vrej Turek Balances of $m$-bonacci Words . . . . . 33--61
Carlos M. da Fonseca Unifying some Pell and Fibonacci
identities . . . . . . . . . . . . . . . 41--42
John Dixon and
Michael Goldenberg and
Ben Mathes and
Justin Sukiennik Triangular truncation of $k$-Fibonacci
and $k$-Lucas circulant matrices . . . . 177--187
Aviezri S. Fraenkel and
Jamie Simpson Corrigendum to ``The exact number of
squares in Fibonacci words'' [Theoret.
Comput. Sci. \bf 218 (1) (1999) 95--106] 122
Esther M. García-Caballero and
Samuel G. Moreno and
Michael P. Prophet A complete view of Vi\`ete-like infinite
products with Fibonacci and Lucas
numbers . . . . . . . . . . . . . . . . 703--711
Ahmet Ipek and
Kamil Ari On Hessenberg and pentadiagonal
determinants related with Fibonacci and
Fibonacci-like numbers . . . . . . . . . 433--439
Max Kanovich Multiset rewriting over Fibonacci and
Tribonacci numbers . . . . . . . . . . . 1138--1151
Thomas Koshy Graph-theoretic models for the Fibonacci
family . . . . . . . . . . . . . . . . . 256--265
Harris Kwong An Alternate Proof of Sury's
Fibonacci--Lucas Relation . . . . . . . 514--514
Florian Luca and
Pantelimon St\uanic\ua On the first digits of the Fibonacci
numbers and their Euler function . . . . 21--25
Florian Luca and
Carl Pomerance On the local behavior of the order of
appearance in the Fibonacci sequence . . 915--933
Rafael Luís and
Henrique M. Oliveira Products of $ 2 \times 2 $ matrices
related to non autonomous Fibonacci
difference equations . . . . . . . . . . 101--116
Surajit Rajagopal and
Martin Griffiths 98.01 On Fibonacci numbers that are
factorials . . . . . . . . . . . . . . . 104--107
José L. Ramírez On convolved generalized Fibonacci and
Lucas polynomials . . . . . . . . . . . 208--213
José L. Ramírez and
Gustavo N. Rubiano and
Rodrigo De Castro A generalization of the Fibonacci word
fractal and the Fibonacci snowflake . . 40--56
José L. Ramírez and
Gustavo N. Rubiano Properties and Generalizations of the
Fibonacci Word Fractal: Exploring
Fractal Curves . . . . . . . . . . . . . ??
B. Sury A Polynomial Parent to a
Fibonacci--Lucas Relation . . . . . . . 236--236
Krasimir Yordzhev Factor-set of binary matrices and
Fibonacci numbers . . . . . . . . . . . 235--238
Jianwei Zhou and
Zhaolin Jiang The spectral norms of $g$-circulant
matrices with classical Fibonacci and
Lucas numbers entries . . . . . . . . . 582--587
Maria Adam and
Nicholas Assimakis and
Alfonso Farina Golden section, Fibonacci sequence and
the time invariant Kalman and Lainiotis
filters . . . . . . . . . . . . . . . . 817--831
Timothy D. Andersen and
Michael Mascagni Memory efficient lagged-Fibonacci random
number generators for GPU supercomputing 163--174
Tianxin Cai and
Deyi Chen and
Yong Zhang Perfect numbers and Fibonacci primes (I) 159--169
Ana Paula Chaves and
Diego Marques A Diophantine equation related to the
sum of powers of two consecutive
generalized Fibonacci numbers . . . . . 1--14
Dennis D. A. Epple and
Jason Siefken Collapse: A Fibonacci and Sturmian Game 515--527
M. Fallahpour and
D. Megias Audio Watermarking Based on Fibonacci
Numbers . . . . . . . . . . . . . . . . 1273--1282
Martin Griffiths Random walks arising from a
Fibonacci's-rabbits scenario . . . . . . 60--67
Kyle Hawkins and
Ursula Hebert-Johnson and
Ben Mathes The Fibonacci identities of
orthogonality . . . . . . . . . . . . . 80--89
Dae S. Hong When Is the Generating Function of the
Fibonacci Numbers an Integer? . . . . . 110--112
Yuke Huang and
Zhiying Wen The sequence of return words of the
Fibonacci sequence . . . . . . . . . . . 106--116
Xiaoyu Jiang and
Kicheon Hong Explicit inverse matrices of Tribonacci
skew circulant type matrices . . . . . . 93--102
Benjamin Keinert and
Matthias Innmann and
Michael Sänger and
Marc Stamminger Spherical Fibonacci mapping . . . . . . 193:1--193:??
Refìk Keskin and
Olcay Karaatli Generalized Fibonacci and Lucas numbers
of the form $ 5 x^2 $ . . . . . . . . . 931--944
Diego Marques A New Fibonacci--Lucas Relation . . . . 683--683
Marc Moyon and
Maryvonne Spiesser L'arithmétique des fractions dans
l'oeuvre de Fibonacci: fondements &
usages . . . . . . . . . . . . . . . . . 391--427
Ayse Nalli and
Cagla Ozyilmaz The third order variations on the
Fibonacci universal code . . . . . . . . 15--32
Raffaele Pisano and
Paolo Bussotti Fibonacci and the Abacus Schools in
Italy. Mathematical Conceptual Streams
--- Education and its Changing
Relationship with Society . . . . . . . 126--164
Carlos Alexis Gómez Ruiz and
Florian Luca On the largest prime factor of the ratio
of two generalized Fibonacci numbers . . 182--203
Aleksander Vesel Linear Recognition and Embedding of
Fibonacci Cubes . . . . . . . . . . . . 1021--1034
Ali Reza Ashrafi and
Jernej Azarija and
Azam Babai and
Khadijeh Fathalikhani and
Sandi Klavzar The (non-)existence of perfect codes in
Fibonacci cubes . . . . . . . . . . . . 387--390
Ay\cse Kurt Bah\csì and
Salih Yalçìnba\cs A New Algorithm for the Numerical
Solution of Telegraph Equations by Using
Fibonacci Polynomials . . . . . . . . . ??
Albrecht Böttcher and
Fuad Kittaneh The limit of the zero set of polynomials
of the Fibonacci type . . . . . . . . . 89--100
Gerth Stòlting Brodal and
Pooya Davoodi and
Moshe Lewenstein and
Rajeev Raman and
Srinivasa Rao Satti Two dimensional range minimum queries
and Fibonacci lattices . . . . . . . . . 33--43
Michaël Cadilhac Review of: \booktitleThe Golden Ratio
and Fibonacci Numbers by Richard A.
Dunlap . . . . . . . . . . . . . . . . . 15--17
Eunice Y. S. Chan and
Robert M. Corless Fibonacci--Mandelbrot polynomials and
matrices . . . . . . . . . . . . . . . . 155--157
Chen Fei Du and
Hamoon Mousavi and
Eric Rowland and
Luke Schaeffer and
Jeffrey Shallit Decision algorithms for
Fibonacci-automatic words, II: Related
sequences and avoidability . . . . . . . 146--162
Chen Fei Du and
Hamoon Mousavi and
Luke Schaeffer and
Jeffrey Shallit Decision Algorithms for
Fibonacci-Automatic Words, III:
Enumeration and Abelian Properties . . . 943--964
Stephan Ramon Garcia and
Florian Luca Quotients of Fibonacci Numbers . . . . . 1039--1044
Keith Johnson and
Kira Scheibelhut Rational Polynomials That Take Integer
Values at the Fibonacci Numbers . . . . 338--346
Emrah Evren Kara and
Merve Ilkhan Some properties of generalized Fibonacci
sequence spaces . . . . . . . . . . . . 2208
Tamara Kogan and
Luba Sapir and
Amir Sapir and
Ariel Sapir The Fibonacci family of iterative
processes for solving nonlinear
equations . . . . . . . . . . . . . . . 148--158
Farshid Mirzaee and
Seyede Fatemeh Hoseini Application of Fibonacci collocation
method for solving Volterra--Fredholm
integral equations . . . . . . . . . . . 637--644
G. P. S. Rathore and
Omprakash Sikhwal and
Ritu Choudhary Generalized Fibonacci Polynomials and
some Identities . . . . . . . . . . . . 4--8
Piotr Slanina Generalizations of Fibonacci polynomials
and free linear groups . . . . . . . . . 187
Gholamreza Talebi and
Mohammad Ali Dehghan Approximation of upper bound for matrix
operators on the Fibonacci weighted
sequence spaces . . . . . . . . . . . . 196
F. V. Weinstein Notes on Fibonacci Partitions . . . . . 482--499
Anupam Das and
Bipan Hazarika Some new Fibonacci difference spaces of
non-absolute type and compact operators 2551--2573
F. Michel Dekking and
Michael S. Keane On the conjugacy class of the Fibonacci
dynamical system . . . . . . . . . . . . 59--69
Sinan Ercan and
Çigdem A. Bektas Some topological and geometric
properties of a new BK-space derived by
using regular matrix of Fibonacci
numbers . . . . . . . . . . . . . . . . 909--921
M. Esmaeili and
M. Moosavi and
T. A. Gulliver A new class of Fibonacci sequence based
error correcting codes . . . . . . . . . 379--396
Markus Grassl and
Andrew J. Scott Fibonacci--Lucas SIC--POVMs . . . . . . 122201
Martin Griffiths 101.44 On a trivariate Fibonacci
identity . . . . . . . . . . . . . . . . 519--522
Thomas Dueholm Hansen and
Haim Kaplan and
Robert E. Tarjan and
Uri Zwick Hollow Heaps . . . . . . . . . . . . . . 42:1--42:??
Myron Hlynka MCMC and the Fibonacci distribution . . 3375--3382
Kimihiko Motegi and
Masakazu Teragaito Generalized Torsion Elements and
Bi-orderability of $3$-manifold Groups 830
Jörg Neunhäuserer Return of Fibonacci random walks . . . . 51--53
Karen Hunger Parshall A plurality of algebras, 1200--1600:
algebraic Europe from Fibonacci to
Clavius . . . . . . . . . . . . . . . . 2--16
Prapanpong Pongsriiam Integral Values of the Generating
Functions of Fibonacci and Lucas Numbers 97--101
Omprakash Sikhwal and
Yashwant Vyas and
Shikha Bhatnagar Generalized Multiplicative Coupled
Fibonacci Sequence and its Properties 14--17
Bartosz Sobolewski The $2$-adic valuation of generalized
Fibonacci sequences with an application
to certain Diophantine equations . . . . 730--742
Marx Stampfli Bridged graphs, circuits and Fibonacci
numbers . . . . . . . . . . . . . . . . 68--79
Owen Toller Book Review: \booktitleFinding Fibonacci
by Keith Devlin, pp. 241, \pounds 24.95,
ISBN 978-0-691-17486-0, Princeton
University Press (2017) . . . . . . . . 569--570
Owen Toller Book Review: \booktitleFinding Fibonacci
by Keith Devlin, pp. 241, \pounds 24.95,
ISBN 978-0-691-17486-0, Princeton
University Press (2017) . . . . . . . . 569--570
Weiping Wang and
Hui Wang Generalized Humbert polynomials via
generalized Fibonacci polynomials . . . 204--216
Xiaoli Ye and
Zhizheng Zhang A common generalization of convolved
generalized Fibonacci and Lucas
polynomials and its applications . . . . 31--37
Argante Ciocci Book Review: \booktitleThe Twelfth
Chapter of Fibonacci's Liber Abaci in
its 1202 version, Bollettino di Storia
delle Scienze Matematiche, by Enrico
Giusti (ed.) . . . . . . . . . . . . . . 137--139
Arzu Coskun and
Necati Taskara A note on the bi-periodic Fibonacci and
Lucas matrix sequences . . . . . . . . . 400--406
Wojciech Florek A class of generalized Tribonacci
sequences applied to counting problems 789--808
Kevin G. Hare and
J. C. Saunders On $ (a, b) $ pairs in random Fibonacci
sequences . . . . . . . . . . . . . . . 352--366
G. J. O. Jameson Fibonacci periods and multiples . . . . 63--76
Issam Kaddoura and
Bassam Mourad On a new improved unifying closed
formula for all Fibonacci-type sequences
and some applications . . . . . . . . . 271--283
Hong Lai and
Mingxing Luo and
Josef Pieprzyk and
Zhiguo Qu and
Mehmet A. Orgun Efficient quantum key distribution using
Fibonacci-number coding with a biased
basis choice . . . . . . . . . . . . . . 24--30
Florian Luca and
Vandita Patel On perfect powers that are sums of two
Fibonacci numbers . . . . . . . . . . . 90--96
Chris D. Lynd and
James Wright Sharpe Sequences Generated by Powers of the
$k$-th-order Fibonacci Recurrence
Relation . . . . . . . . . . . . . . . . 443--446
Michel Mollard The existence of perfect codes in a
family of generalized Fibonacci cubes ii--ii
János Podani and
Ádám Kun and
András Szilágyi How Fast Does Darwin's Elephant
Population Grow? . . . . . . . . . . . . 259--281
Tim Price Proof Without Words: Sum of Squares of
Consecutive Fibonacci Numbers . . . . . 121--121
Carlos Alexis Gómez Ruiz and
Florian Luca On prime factors of the sum of two
$k$-Fibonacci numbers . . . . . . . . . 1171--1195
Bernard Rybolowicz and
Agnieszka Tereszkiewicz Generalized tricobsthal and generalized
tribonacci polynomials . . . . . . . . . 297--308
J. A. Scott 102.04 On the series of Fibonacci
reciprocals . . . . . . . . . . . . . . 100--102
Richard Simpson Book Review: \booktitleFinding
Fibonacci: the quest to rediscover the
forgotten mathematical genius who
changed the world, by Keith Devlin . . . 136--137
Jizhen Yang and
Zhizheng Zhang Some identities of the generalized
Fibonacci and Lucas sequences . . . . . 441--450
Pierre Bonardo and
Anna E. Frid and
Jeffrey Shallit The number of valid factorizations of
Fibonacci prefixes . . . . . . . . . . . 68--75
Zhaodong Cai and
A. J. Hildebrand and
Junxian Li A local Benford Law for a class of
arithmetic sequences . . . . . . . . . . 613--638
Krishnendu Chatterjee and
Hongfei Fu and
Amir Kafshdar Goharshady Non-polynomial Worst-Case Analysis of
Recursive Programs . . . . . . . . . . . 20:1--20:??
Amy Glen and
Jamie Simpson and
W. F. Smyth More properties of the Fibonacci word on
an infinite alphabet . . . . . . . . . . 301--311
C. Gueunet and
P. Fortin and
J. Jomier and
J. Tierny Task-Based Augmented Contour Trees with
Fibonacci Heaps . . . . . . . . . . . . 1889--1905
Bir Kafle and
Florian Luca and
Amanda Montejano and
László Szalay and
Alain Togbé On the $X$-coordinates of Pell equations
which are products of two Fibonacci
numbers . . . . . . . . . . . . . . . . 310--333
Emrah Kiliç and
Talha Arikan A nonlinear generalization of the
Filbert matrix and its Lucas analogue 141--157
K. Kuhapatanakul and
K. Thongsing Generalizations of the Fibonacci--Lucas
Relations . . . . . . . . . . . . . . . 81--81
Rick Mabry Fibonacci Numbers, Integer Compositions,
and Nets of Antiprisms . . . . . . . . . 786--801
Andre A. Marinho and
Francisco A. Brito Hermite polynomials and Fibonacci
oscillators . . . . . . . . . . . . . . 012101
K. B. Subramaniam 103.28 On a link between Triangular and
Fibonacci numbers . . . . . . . . . . . 489--489
Gholamreza Talebi and
Mohammad Ali Dehghan Approximation of upper bound for matrix
operators on the Fibonacci weighted
sequence spaces . . . . . . . . . . . . 1717--1718
Bruce Torrence Passing the Buck and Firing Fibonacci:
Adventures with the Stochastic Abacus 387--399
Alaa Altassan and
Florian Luca On the equation $ \sum_{j = 1}^k j F_j^p
= F_n^q $ . . . . . . . . . . . . . . . 256--277
Fan Chung and
Ron Graham and
Sam Spiro Slow Fibonacci walks . . . . . . . . . . 142--170
Mahadi Ddamulira and
Florian Luca On the problem of Pillai with
$k$-generalized Fibonacci numbers and
powers of $3$ . . . . . . . . . . . . . 1643--1666
Michel Dekking Morphic words, Beatty sequences and
integer images of the Fibonacci language 407--417
Ömer E\ugecio\uglu and
Elif Saygì and
Zülfükar Saygì $k$-Fibonacci Cubes: A Family of
Subgraphs of Fibonacci Cubes . . . . . . 639--661
Jesus Guillera When Ramanujan Meets Fibonacci and Lucas 159--159
Oguz Ogur Superposition operators on sequence
spaces $ \ell_p(F) $ derived by using
matrix of Fibonacci numbers . . . . . . 2087--2098
Wayne Peng ABC implies there are infinitely many
non--Fibonacci--Wieferich primes . . . . 354--375
Jawad Sadek and
Russell Euler 104.03 On periods of Fibonacci numbers
using modular arithmetic on the Binet
formula . . . . . . . . . . . . . . . . 150--154
Jawad Sadek and
Russell Euler 104.26 Unusual Fibonacci, Lucas and Pell
congruence relations . . . . . . . . . . 507--509
Szabolcs Tengely and
MacIej Ulas The Diophantine equation $ F_n = P(x) $ 2095--2111
Xiao-Xin Zhao and
Wen-Feng Qi and
Jia-Min Zhang Further results on the equivalence
between Galois NFSRs and Fibonacci NFSRs 153--171
Enide Andrade and
Dante Carrasco-Olivera and
Cristina Manzaneda On circulant like matrices properties
involving Horadam, Fibonacci, Jacobsthal
and Pell numbers . . . . . . . . . . . . 100--120
Norman Biggs Linear Programming from Fibonacci to
Farkas . . . . . . . . . . . . . . . . . 1--21
Jhon J. Bravo and
Jose L. Herrera and
Florian Luca Common values of generalized Fibonacci
and Pell sequences . . . . . . . . . . . 51--71
Sam Chow and
Tom Slattery On Fibonacci partitions . . . . . . . . 310--326
Ömer E\ugecio\uglu and
Elif Sayg\i and
Zülfükar Sayg\i The number of short cycles in Fibonacci
cubes . . . . . . . . . . . . . . . . . 134--146
Carlos A. Gómez and
Jhonny C. Gómez and
Florian Luca Two $b$-repunits in the Fibonacci
sequence . . . . . . . . . . . . . . . . 393--422
Martin Griffiths 105.01 On some composite Fibonacci
expressions . . . . . . . . . . . . . . 106--108
Josh Hiller Fibonacci's Bunny-pocalypse! . . . . . . 78--78
Anuradha Jagannathan The Fibonacci quasicrystal: Case study
of hidden dimensions and multifractality 045001
Salima Kebli and
Omar Kihel and
Jesse Larone and
Florian Luca On the nonnegative integer solutions to
the equation $ F_n \pm F_m = y^a $ . . . 107--127
Sachin Kumar Image data security using Quasigroup
combined with Fibonacci Q-transformation ??
Zhixin Liu and
Mengyuan Xue The sum of a prime and a Fibonacci
number . . . . . . . . . . . . . . . . . 1815--1823
R. Marques and
C. Bouville and
K. Bouatouch and
J. Blat Extensible Spherical Fibonacci Grids . . 2341--2354
Haifa Aldossari and
Michael Mascagni Scrambling additive lagged-Fibonacci
generators . . . . . . . . . . . . . . . ??
Jean-Luc Baril and
Sergey Kirgizov and
Vincent Vajnovszki Gray codes for Fibonacci $q$-decreasing
words . . . . . . . . . . . . . . . . . 120--132
A. F. Beardon 106.33 Fibonacci numbers and Cassini's
identity . . . . . . . . . . . . . . . . 498--501
Alireza Etminaniesfahani and
Hanyu Gu and
Amir Salehipour ABFIA: a hybrid algorithm based on
artificial bee colony and Fibonacci
indicator algorithm . . . . . . . . . . ??
Menso Folkerts Book Review: \booktitleLeonardi Bigolli
Pisani vulgo Fibonacci. Liber Abbaci
(Biblioteca di Nuncius; vol. 79) by
Enrico Giusti, Paolo d'Alessandro . . . 123--125
Paolo Freguglia A New Edition of Leonardo Fibonacci's
\booktitleLiber Abbaci . . . . . . . . . 207--213
Peter Hall Book Review: \booktitleFibonacci's
rabbits by Adam Hart-Davis, pp. 176,
\pounds 12.99 (paper), ISBN
978-1-912827-03-9, Modern Books (2019) 191--191
Kevin Hare and
J. C. Saunders Generalised Fibonacci sequences
constructed from balanced words . . . . 349--377
Marieh Jahannia and
Morteza Mohammad-Noori and
Narad Rampersad and
Manon Stipulanti Closed Ziv--Lempel factorization of the
$m$-bonacci words . . . . . . . . . . . 32--47
Mohammad Javaheri and
Stephanie Cambrea The Distribution of Fibonacci Numbers
Modulo Primes . . . . . . . . . . . . . 75--79
Howard Sporn Fibonacci Fraction Circles . . . . . . . 1--8
Howard Sporn Fibonacci--Lucas hyperbolas . . . . . . 242--246
Sara Barrows and
Emily Noye and
Sarah Uttormark and
Matthew Wright Three's A Crowd: an Exploration of
Subprime Tribonacci Sequences . . . . . 464--475
John P. Bonomo and
Montana Ferita A Small Fib . . . . . . . . . . . . . . 274--289
B. He and
Y. L. Mao and
A. Togbé A Fibonacci Version of Wolstenholme's
Harmonic Series Congruence . . . . . . . 83--85
Jeffrey Shallit Note on a Fibonacci parity sequence . . 309--315
Zhengyuan Shi and
Cheng Chen and
Gangqiang Yang and
Hailiang Xiong and
Fudong Li and
Honggang Hu and
Zhiguo Wan Design Space Exploration of Galois and
Fibonacci Configuration Based on
Espresso Stream Cipher . . . . . . . . . 43:1--43:??
Seán M. Stewart 107.01 A simple integral representation
of the Fibonacci numbers . . . . . . . . 120--123
Hans J. H. Tuenter In Search of Comrade Agronomof: Some
Tribonacci History . . . . . . . . . . . 708--719
Holly-Anne Turner and
Matthew Humpage and
Hans Kerp and
Alexander J. Hetherington Leaves and sporangia developed in rare
non-Fibonacci spirals in early leafy
plants . . . . . . . . . . . . . . . . . 1188--1192
Attila Bérczes and
István Pink and
Paul Thomas Young Cullen numbers and Woodall numbers in
generalized Fibonacci sequences . . . . 86--102
Hannah Blasiyus and
D. K. Sheena Christy Palindromes in involutive Fibonacci
arrays . . . . . . . . . . . . . . . . . 22520--22547
Sam Chow and
Owen Jones On the variance of the Fibonacci
partition function . . . . . . . . . . . 341--353
L'ubomíra Dvo\vráková and
Edita Pelantová An upper bound on asymptotic repetition
threshold of balanced sequences via
colouring of the Fibonacci sequence . . ??
Manohara G. and
Kumbinarasaiah S. An innovative Fibonacci wavelet
collocation method for the numerical
approximation of Emden--Fowler equations 347--369
Jonathan García and
Carlos A. Gómez and
Florian Luca Solving Skolem's problem for the
$k$-generalized Fibonacci sequence with
negative indices . . . . . . . . . . . . 273--299
Jon Grantham and
Andrew Granville Fibonacci primes, primes of the form $
2^n - k $ and beyond . . . . . . . . . . 190--219
V. L. Kulikov and
E. F. Olekhova and
V. I. Oseledets On Absolute Continuity of the Erd\Hos
Measure for the Golden Ratio, Tribonacci
Numbers, and Second-Order Markov Chains 265--280
G. Manohara and
S. Kumbinarasaiah Fibonacci wavelet collocation method for
the numerical approximation of
fractional order Brusselator chemical
model . . . . . . . . . . . . . . . . . 2651--2681
Yingyin Pan and
Jianghua Zhong and
Dongdai Lin The equivalence between Galois and
Fibonacci NFSRs . . . . . . . . . . . . ??
Yingyin Pan and
Jianghua Zhong and
Dongdai Lin Generalized cycle joining method and its
application to the construction of
long-period Galois NFSRs . . . . . . . . 4287--4311
Manpal Singh and
S. Das and
Rajeev An innovative Vieta--Fibonacci wavelet
collocation method for the numerical
solution of three-component Brusselator
reaction diffusion system of fractional
order . . . . . . . . . . . . . . . . . 1558--1594