Applications of Fibonacci Numbers

Bergum, Gerald E.; Philippou, Andreas N.; Horadam, Alwyn F.

Applications of Fibonacci Numbers

Edited by Gerald E. Bergum, Andreas N. Philippou and Alwyn F. Horadam

in Springer Books from Springer

Date: 1993
ISBN: 978-94-011-2058-6
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Chapters in this book:

Multidimensional Golden Means: Peter G. Anderson
A Necessary and Sufficient Condition that Rays of a Star Configuration on Pascal’s Triangle Cover its Center with Respect to GCD and LCM: Shiro Ando and Daihachiro Sato
On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and its Generalizations: Shiro Ando and Daihachiro Sato
An Extension of an Old Classical Diophantine Problem: Joseph Arkin, David C. Arney, Frank R. Giordano, Rickey A. Kolb and Gerald E. Bergum
Fourier Analysis in Finite Nilpotent Groups: Huseyin Aydin and Geoff C. Smith
Wall and Vinson Revisited: Huseyin Aydin, Ramazan Dikici and Geoff C. Smith
Designer Decimals: Fractions which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left: Marjorie Bicknell-Johnson
Semigroup Presentations and Number Sequences: Colin M. Campbell, Edmund F. Robertson and Richard M. Thomas
Counting the Number of Solutions of Congruences: Umberto Cerruti
On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials: O. Chryssaphinou, S. Papastavridis and T. Tsapelas
Embedding Fibonacci Words into Fibonacci Word Patterns: Wai-fong Chuan
On Sums of Cubes of Fibonacci Numbers: Stuart Clary and Paul D. Hemenway
Integer Sided Triangles Whose Ratio of Altitude to Base is an Integer: Charles K. Cook and Gerald E. Bergum
On a Class of Iterative Recurrence Relations: Karl Dilcher
Discrete Operational Calculi for Two-sided Sequences: Ivan H. Dimovski and Virginia S. Kiryakova
Transformations of Fibonacci-Lucas Identities: L. A. G. Dresel
Fibonacci Numbers and Continued Fraction Expansions: Michael Drmota
The DFF and DFFz Triangles and Their Mathematical Properties: Marco Faccio, Giuseppe Ferri and Arnaldo D’Amico
Contributions from Cascaded Combinations to the Naming of Special Permutations: Daniel C. Fielder and Cecil O. Alford
The Zeckendorf Representation of {F kn /F n }: Piero Filipponi and Herta T. Freitag
Fractal Patterns Derived from Rational Binomial Coefficients: Dan Flath and Rhodes Peele
Hausdorff Dimension in Pascal’s Triangle: Dan Flath and Rhodes Peele
Chaos, Elliptic Curves and All That: Matthew Fletcher and Geoff C. Smith
Co-Related Sequences Satisfying the General Second Order Recurrence Relation: H. T. Freitag and G. M. Phillips
On the Moments of the Sum-of-Digits Function: P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy
Problems on Fibonacci and B-Adic Tree Representations by Regular K-Gons: Heiko Harborth
Two-Distance Sets and the Golden Ratio: Heiko Harborth and Lothar Piepmeyer
A Fibonacci Problem Classification Scheme Useful to Undergraduate Pedagogy: Russell Jay Hendel
Zeckendorf Representations of Positive and Negative Integers by Pell Numbers: A. F. Horadam
Integration Sequences of Fibonacci and Lucas Polynomials: Alwyn F. Horadam and Piero Filipponi
Pell-Type Number Generators of Pythagorean Triples: A. F. Horadam and A. G. Shannon
Balance Morphology of a Binary Tree: Yasuichi Horibe
Nörlund’s Number Bn (n): F. T. Howard
On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials: Leetsch C. Hsu
A Sequence Arising from Reflections in Multiple Glass Plates: Naotaka Imada
Diophantine Representation of Non-Fibonacci Numbers: James P. Jones
On Some Problems Related to the Fibonacci Group: Ann Chi Kim
Congruence Properties of Fibonacci Numbers and Fibonacci Coefficients Modulo p2: William A. Kimball and William A. Webb
Orderings of the Set of All Positive Fibonacci Sequences: Clark Kimberling
Some Results Concerning the Reciprocal Sum of Prime Divisors of a Lucas Number: Peter Kiss
Rational Numbers with Predictable Engel Product Expansions: Arnold Knopfmacher
Two Families of Orthogonal Polynomial Systems Related to Fibonacci Chains: Wolfdieter Lang
On the Formation of Higher Order Higher Dimensional Line-Sequential Vector Spaces: Jack Y. Lee
Arithmetic Sequences and Second order Recurrences: Calvin Long, Graeme L. Cohen, Timothy Langtry and A. G. Shannon
Generalized Fibonacci Pseudoprimes and Probable Primes: Winfried B. Müller and Alan Oswald
A Generalization of the Fibonacci Sequence: S. P. Pethe and C. N. Phadte
How to Advance on a Stairway by Coin Flippings: Helmut Prodinger
Fibonacci Sequence and its Generalizations Hidden in Algorithms for Generating Morse Codes: Shuichi Sato
On Matrix Representations of Generalized Fibonacci Numbers and Their Applications: Shuichi Sato
A Cholesky Decomposition in Matching Insulin Profiles: A. G. Shannon, R. L. Ollerton and D. R. Owens
Generalized Exponential and Trigonometric Functions: John C. Sjoberg
Divisibility of Terms in Lucas Sequences by Their Subscripts: Lawrence Somer
Upper Bounds for Frequencies of Elements in Second-Order Recurrences over A Finite Field: Lawrence Somer
On the Convergence of Quotients of Some Recursive Sequences: Lea Terracini
Two Distribution Problems for Polynomials: Robert F. Tichy
The Elements of Enteger Geometry: J. C. Turner and A. G. Schaake
Totient Functions on the Euler Number Tree: J. C. Turner, H. Garcia and A. G. Schaake
Using Matrix Techniques to Establish Properties of k-Order Linear Recursive Sequences: Marcellus E. Waddill

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DOI: 10.1007/978-94-011-2058-6

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