Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xxiv

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2. On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences

   • Shiro Ando, Daihachiro Sato

   Pages 1-10

3. On Triangles and Squares Marked with Goldpoints—Studies of Golden Tiles

   • Vassia K. Anatassova, J. C. Turner

   Pages 11-25

4. Multivariate Pascal Polynomials of Order K with Probability Applications

   • Demetrios L. Antzoulakos, Andreas N. Philippou

   Pages 27-41

5. Fibonacci Planes and Spaces

   • K. T. Atanassov, A. G. Shannon

   Pages 43-46

6. The Smallest Positive Integer Having Fk Representations as Sums of Distinct Fibonacci Numbers

   • Marjorie Bicknell-Johnson

   Pages 47-52

7. The Zeckendorf-Wythoff Array Applied to Counting the Number of Representations of N as Sums of Distinct Fibonacci Numbers

   • Marjorie Bicknell-Johnson

   Pages 53-60

8. Composing with Sequences: …But is It Art?

   • John A. Biles

   Pages 61-73

9. Invariants for Linear Recurrences

   • Mihai Caragiu, William Webb

   Pages 75-81

10. Base 10 RATS Cycles and Arbitrarily Long Base 10 RATS Cycles

    • Curtis Cooper, Robert E. Kennedy

    Pages 83-93

11. Quintics x5-5x-k, the Golden Section, and Square Lucas Numbers

    • Michele Elia, Piero Filipponi

    Pages 95-101

12. The Pascal-De Moivre Moments and Their Generating Functions

    • Larry Ericksen

    Pages 103-120

13. Investigating Special Binary Sequences with Some Computer Help

    • Daniel C. Fielder, Cecil O. Alford

    Pages 121-128

14. Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials

    • Piero Filipponi, Alwyn F. Horadam

    Pages 129-139

15. A Property of the Unit Digits of Recursive Sequences

    • Herta T. Freitag, Marjorie Bicknell-Johnson, George M. Phillips

    Pages 141-148

16. On General Divisibility of Sums of Integral Powers of the Golden Ratio

    • Herta T. Freitag, Daniel C. Fielder

    Pages 149-154

17. Sylvester’s Algorithm and Fibonacci Numbers

    • Herta T. Freitag, George M. Phillips

    Pages 155-163

18. On the Characteristic Polynomial of the j-TH Order Fibonacci Sequence

    • George W. Grossman, Sivaram K. Narayan

    Pages 165-177

19. Quasi Morgan-Voyce Polynomials and Pell Convolutions

    • A. F. Horadam

    Pages 179-193

20. On an Asymptotic Maximality of the Fibonacci Tree

    • Yasuichi Horibe

    Pages 195-200

This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its seven predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 1, 1999 The Editor F. T. Howard Mathematics and Computer Science Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC USA xvii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Anderson, Peter G. , Chairman Horadam, A. F. (Australia), Co-Chair Arpaya, Pasqual Philippou, A. N. (Cyprus), Co-Chair Biles, John Bergum, G. E. (U. S. A. ) Orr, Richard Filipponi, P. (Italy) Radziszowski, Stanislaw Harborth, H. (Germany) Rich, Nelson Horibe, Y. (Japan) Howard, F. (U. S. A. ) Johnson, M. (U. S. A. ) Kiss, P. (Hungary) Phillips, G. M. (Scotland) Turner, J. (New Zealand) Waddill, M. E. (U. S. A. ) xix LIST OF CONTRIBUTORS TO THE CONFERENCE AGRATINI, OCTAVIAN, "Unusual Equations in Study. " *ANDO, SHIRO, (coauthor Daihachiro Sato), "On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences. " *ANATASSOVA, VASSIA K. , (coauthor J. C.

• Prime
• Prime number
• algorithms
• combinatorics
• computer
• geometry
• number theory
• probability

• Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, USA

  Fredric T. Howard

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