Fibonacci Quarterly | Books & Tables
Fibonacci Association

A Collection of Manuscripts Related to the Fibonacci Sequence

18th Anniversary Volume

Edited by Verner E. Hoggatt, Jr. and Marjorie Bicknell-Johnson

Published 1980 by the Fibonacci Association

You may download the entire volume (size: 21Mb) for free, or individual articles below.

CONTENTS

Title Page

Preface
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Table of Contents
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Paul J. Campbell & Christopher Moeller
Secondary Fibonacci Sequences
1
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F. Schweiger
An Estimate for the Length of a Finite Jacobi Algorithm
16
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Jaques Troué
Solution of the Recurrent Equation un+1=2un-un-1+un-3
18
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Richard C. Weimer
Primeness for the Gaussian Integers
19
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Richard C. Weimer
A Note on Ordering the Complex Numbers
20
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Jerome Hines
Theory of Extra Numerical Information Applied to the Fibonacci Sum
22
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Paul N. Mendelsohn
The Pentanacci Numbers
31
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George Berzsenyi
Remarks on the Diophantine Equations a2±ab+b2 =c2
34
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A. M. Russell
Triangular Displays of Integers
38
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Louise S. Grinstein
Pythagorean Triangles and Multiple Angles
39
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Curtis R. Vogel
Proof that the Area of a Pythagorean Triangle is Never a Square
43
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Jan van Leeuwen
Reconsidering a Problem of M. Ward
45
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Jerry T. Sullivan
What a Difference a Difference Makes!
46
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Jerome Minkus
Circulants and Horadam's Sequences
48
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Loren L. Dickerson
An Expansion of Golubev's 11 x 11 Magic Square of Primes to Its Maximum, 21 x 21
52
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John R. Howell
Some Extensions of Properties of the Sequence of Fibonacci Polynomials
54
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Carl S. Weisman
A Divisibility Property of Binomial Coefficients
57
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Arthur F. Setteducati
Fibonacci Fever
58
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Rodney T. Hansen
Exponential Generation of Basic Linear Identities
61
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H. V. Krishna
Identities of a Generalized Fibonacci Sequence
65
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H. V. Krishna
Divisibility Properties of a Generalized Fibonacci Sequence
66
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H. V. Krishna
Pythagorean Pentids
67
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Jeffrey Shallit
A Triangle for the Bell Numbers
69
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Manoranjitham Veluppillai
The equations z2-3y2=-2 and z2-6x2=-5
71
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Salah M. Yousif
Generation of Fibonacci Numbers by Digital Filters
75
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Charles F. Winans
The Fibonacci Series in the Decimal Equivalents of Fractions
78
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Paul S. Bruckman
Generalization of a Problem of Gould and Its Solution by a Contour Integral
82
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Charles W. Trigg
A Miscellany of 1979 Curiosa
87
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Charles W. Trigg
101 Faces of 1979
88
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Charles W. Trigg
Determinants Related to 1979
89
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Charles W. Trigg
Reiterative Routines Applied to 1979
90
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Charles W. Trigg and Avetta Trigg
1979 and Associated Primes
91
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Charles W. Trigg
The Powerful 1979
93
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M. G. Monzingo
An Observation Concerning Whitford's "Binet's Formula Generalized"
93
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M. G. Monzingo
On the Distribution of Quadratic Residues
94
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David Singmaster
Divisibility of Binomial and Multinomial Coefficients by Primes and Prime Powers
98
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Verner E. Hoggatt, Jr. and Marjorie Bicknell-Johnson
A Matrix Generation of Fibonacci Identities for F2nk
114
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Charles W. Trigg
Antimagic Pentagrams With Line Sums in Arithmetic Progression, Δ=3
124
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Charles W. Trigg
Two Families of Twelfth-Order Magic Squares
127
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Carl P. McCarty
Coin Tossing and the r-bonacci Numbers
130
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Susan C. Seeder
Combinatorial Identities Derived from Units
132
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David R. Morrison
A Stolarsky Array of Wythoff Pairs
134
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Jerome D. Braverman and David J. Toof
An Application of the Fibonacci Search Technique to Determine Optimal Sample Size in a Bayesian Decision Problem
137
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Ralph Gellar
Simultaneous Tribonacci Representations
145
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Gregory Wulczyn
Polynomial Fibonacci-Lucas Identities of the Form ∑r=1nP(r)Fr
157
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Gregory Wulczyn
A Generalization of Some L. Carlitz Identities
159
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John Konvalina
A Characterization of the Pythagorean Triples
160
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Seppo Pajunen
On Primitive Weird Numbers
162
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Kesar Singh
Fibonacci Concept: Extension to Real Roots of Polynomial Equations
166
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D. G. Rogers
Triangular Arrays Associated With Some Partitions
169
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H. N. Malik and A. Qadir
Break-up Integers and Bracket Functions in Terms of Bracket Functions
172
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H. N. Malik and A. Qadir
Pseudo-Periodic Difference Equations
176
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H. N. Malik and A. Qadir
solutions of Pseudo-Periodic Difference Equations
179
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S. P. Mohanty
A Class of Diophantine Equations
186
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János Surányi
A Divisibility Property Concerning Binomial Coefficients
189
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Gregory Wulczyn
Formation of Generalized F-L Identities of the Form ∑r=1nrsFkr+a
192
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Gregory Wulczyn
Generalized Fibonacci-Lucas Difference Equations
202
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David W. Wall
Conditions for Φ(N) to properly divide N-1
205
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Ray Steiner
On Fibonacci Numbers of the Form x2+1
208
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Robert J. Kinney
Fibonacci Sequence Can Serve Physicians and Biologists
210
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H. Turner Laquer
Values of Circulants With Integer Entries
212
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William H. Cornish
Powers of Matrices and Recurrence Relations
217
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Ralph Fecke
Convergence Properties of Linear Recursion Sequences
223
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