Applications of Fibonacci Numbers
Editor
- Gerald E. Bergum(South Dakota State University, Computer Science Department)Andreas N. PhilippouAlwyn F. Horadam(The University of New England, Department of Mathematics, Statistics and Computer Science)
Abstract
Individual chapters are listed in the "Chapters" tab
Suggested Citation
DOI: 10.1007/978-94-009-0223-7
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Book Chapters
The following chapters of this book are listed in IDEAS- Peter G. Anderson, 1996. "Advances in Linear Pixel Shuffling," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 1-21, Springer.
- Shiro Ando & Daihachiro Sato, 1996. "Minimal Center Covering Stars with Respect to LCM in Pascal’s Pyramid and its Generalizations," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 23-30, Springer.
- Shiro Ando & Daihachiro Sato, 1996. "Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 31-45, Springer.
- John R. Burke, 1996. "Some Remarks on the Distribution of Second Order Recurrences and a Related Group Structure," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 47-52, Springer.
- Umberto Cerruti & Francesco Vaccarino, 1996. "Matrices, Recurrent Sequences and Arithmetic," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 53-62, Springer.
- Umberto Cerruti & Francesco Vaccarino, 1996. "Vector Linear Recurrence Sequences in Commutative Rings," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 63-72, Springer.
- Wai-fong Chuan, 1996. "Subwords of the Golden Sequence and the Fibonacci Words," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 73-84, Springer.
- M. N. Deshpande & G. E. Bergum, 1996. "Interesting Arrays Associated with Fibonacci Sequences," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 85-92, Springer.
- Daniel C. Fielder & Cecil O. Alford, 1996. "More Applications of a Partition Driven Symmetric Table," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 93-103, Springer.
- Piero Filipponi & Alwyn F. Horadam, 1996. "Partial Derivative Sequences of Second-Order Recurrence Polynomials," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 105-122, Springer.
- Piero Filipponi & Herta T. Freitag, 1996. "The Zeckendorf Decomposition of Certain Classes of Integers," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 123-135, Springer.
- H. T. Freitag & G. M. Phillips, 1996. "On the Sum of Consecutive Squares," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 137-142, Springer.
- Heiko Harborth & Silke Maasberg, 1996. "Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 143-153, Springer.
- Heiko Harborth & Lothar Piepmeyer, 1996. "Rooks on Fibonacci Boards," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 155-163, Springer.
- E. O. Hare & P. Z. Chinn, 1996. "Tiling with Cuisenaire Rods," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 165-171, Springer.
- Russell Jay Hendel, 1996. "Hofstadter’s Conjecture for $$\alpha = \sqrt 2 - 1$$," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, chapter 16, pages 173-199, Springer.
- Russell Jay Hendel & Charles K. Cook, 1996. "Recursive Properties of Trigonometric Products," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, chapter 17, pages 201-214, Springer.
- A. F. Horadam, 1996. "A Synthesis of Certain Polynomial Sequences," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 215-229, Springer.
- A. F. Horadam, 1996. "Minmax Sequences for Pell Numbers," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 231-249, Springer.
- Yasuichi Horibe, 1996. "On Dichotomous Complexity of the Fibonacci Tree," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 251-256, Springer.
- Fred T. Howard, 1996. "Formulas of Ramanujan Involving Lucas Numbers, Pell Numbers, and Bernoulli Numbers," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 257-270, Springer.
- Derek Jennings, 1996. "Counting Sets of Integers with Various Summation Properties," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 271-281, Springer.
- William A. Kimball, 1996. "Factorials & Binomial Coefficients in Polynomial Rings Over Finite Fields," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 283-290, Springer.
- Z. F. Koçak & G. M. Phillips, 1996. "An Identity Involving the q-Factorial," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 291-296, Springer.
- Ed Korntved, 1996. "GCD Properties of an Octagon," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 297-302, Springer.
- Joseph Lahr, 1996. "Products and Quotients of Difference Equations," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 303-320, Springer.
- Wolfdieter Lang, 1996. "The Wythoff and the Zeckendorf Representations of Numbers are Equivalent," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 321-337, Springer.
- Jack Y. Lee, 1996. "Some Basic Translational Properties of the General Fibonacci Line-Sequence," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 339-347, Springer.
- Ming Luo, 1996. "Pentagonal Numbers in the Fibonacci Sequence," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 349-354, Springer.
- R. S. Melham & A. G. Shannon, 1996. "On Reciprocal Sums of Second Order Sequences," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 355-364, Springer.
- Walter Oberschelp, 1996. "Solving Linear Recurrences from Differential Equations in the Exponential Manner and Vice Versa," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 365-380, Springer.
- Blake E. Peterson & James H. Jordan, 1996. "The Rational Heart of the Integer Fibonacci Pentagons," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 381-388, Springer.
- Stanley Rabinowitz, 1996. "Algorithmic Manipulation of Fibonacci Identities," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 389-408, Springer.
- A. Rotkiewicz, 1996. "On Lucas Pseudoprimes of the Form ax 2 + bxy + cy 2," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 409-421, Springer.
- Ken-ichi Sato & Susumu Shirai, 1996. "N Certain Rational Expressions whose Prime Divisors are Cubic Residues (Mod P)," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 423-429, Springer.
- A. G. Shannon & R. P. Loh & R. S. Melham & A. F. Horadam, 1996. "A Search for Solutions of a Functional Equation," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 431-441, Springer.
- A. G. Shannon & Irving C. Tang & R. L. Ollerton, 1996. "A Use of Generalized Fibonacci Numbers in Finding Quadratic Factors," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 443-450, Springer.
- Lawrence Somer, 1996. "Distribution of Residues of Certain Second-Order Linear Recurrences Modulo p-III," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 451-471, Springer.
- Lawrence Somer, 1996. "Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 473-486, Springer.
- J. C. Turner & A. G. Schaake, 1996. "On a Model of the Modular Group," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 487-504, Springer.
- Marcellus E. Waddill, 1996. "Properties of a k-Order Linear Recursive Sequence Modulo m," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 505-519, Springer.
- Diana L. Wells, 1996. "Residue Counts Modulo Three for the Fibonacci Triangle," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 521-536, Springer.
- Paul Thomas Young, 1996. "On a Class of Congruences for Lucas Sequences," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 537-544, Springer.
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