Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xxxiii

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2. Universal Bernoulli Polynomials and P-Adic Congruences

   • Arnold Adelberg

   Pages 1-8

3. A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties

   • Octavian Agratini

   Pages 9-18

4. Fibinomial Identities

   • Arthur T. Benjamin, Jennifer J. Quinn, Jeremy A. Rouse

   Pages 19-24

5. Recounting Binomial Fibonacci Identities

   • Arthur T. Benjamin, Jeremy A. Rouse

   Pages 25-28

6. The Fibonacci Diatomic Array Applied to Fibonacci Representations

   • Marjorie Bicknell-Johnson

   Pages 29-38

7. On Purple Parrots, Fibonacci Numbers, and Color Theory

   • Marjorie Bicknell-Johnson

   Pages 39-42

8. Finding Fibonacci in a Fractal

   • Nathan C. Blecke, Kirsten Fleming, George William Grossman

   Pages 43-62

9. Positive Integers (a ² + b ²)/(ab + 1) are Squares

   • Jens-P. Bode, Heiko Harborth

   Pages 63-67

10. On the Fibonacci Length of Powers of Dihedral Groups

    • C. M. Campbell, P. P. Campbell, H. Doostie, E. F. Robertson

    Pages 69-85

11. Some Sums Related to Sums of Oresme Numbers

    • Charles K. Cook

    Pages 87-99

12. Some Thoughts on Rook Polynomials on Square Chessboards

    • Dan Fielder

    Pages 101-108

13. Pythagorean Quadrilaterals

    • Robert Hochberg, Glenn Hurlbert

    Pages 109-119

14. A General Lacunary Recurrence Formula

    • F. T. Howard

    Pages 121-135

15. Ordering Words and Sets of Numbers: The Fibonacci Case

    • Clark Kimberling

    Pages 137-144

16. Some Basic Properties of a Tribonacci Line-Sequence

    • Jack Y. Lee

    Pages 145-157

17. A Type of Sequence Constructed from Fibonacci Numbers

    • Aihua Li, Sindhu Unnithan

    Pages 159-166

18. Cullen Numbers in Binary Recurrent Sequences

    • Florian Luca, Pantelimon Stănică

    Pages 167-175

19. A Generalization of Euler’s Formula and its Connection to Fibonacci Numbers

    • Jonathan F. Mason, Richard H. Hudson

    Pages 177-185

20. Extensions of Generalized Binomial Coefficients

    • Richard L. Ollerton, Anthony G. Shannon

    Pages 187-199

This book contains 28 research articles from among the 49 papers and abstracts presented at the Tenth International Conference on Fibonacci Numbers and Their Applications. These articles have been selected after a careful review by expert referees, and they range over many areas of mathematics. The Fibonacci numbers and recurrence relations are their unifying bond. We note that the article "Fibonacci, Vern and Dan" , which follows the Introduction to this volume, is not a research paper. It is a personal reminiscence by Marjorie Bicknell-Johnson, a longtime member of the Fibonacci Association. The editor believes it will be of interest to all readers. It is anticipated that this book, like the eight predecessors, will be useful to research workers and students at all levels who are interested in the Fibonacci numbers and their applications. March 16, 2003 The Editor Fredric T. Howard Mathematics Department Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Calvin Long, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv LIST OF CONTRlBUTORS TO THE CONFERENCE * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, ART, "Mathemagics.

• Partition
• combinatorics
• cryptography
• geometry
• number theory
• sets

• Wake Forest University, Winston-Salem, USA

  Frederic T. Howard

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