Applications of Fibonacci Numbers, 1999
Volume 8: Proceedings of The Eighth International Research Conference on Fibonacci Numbers and Their Applications

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.

A Report on the Eighth International Conference. List of Contributors to this Proceedings. Foreword. The Organizing Committees. List of Contributors to the Conference. Introduction. On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences; S. Ando, D. Sato. On Triangles and Squares Marked with Goldpoints-Studies of Golden Tiles; V.K. Anatassova, J.C. Turner. Multivariate Pascal Polynomials or order K with Probability Applications; D.L. Antzoulakos, A.N. Philippou. Fibonacci Planes and Spaces; K.T. Atanassov, A.G. Shannon. The Smallest Positive Integer Having Fk Representations as Sums of Distinct Fibonacci Numbers; M. Bicknell-Johnson. The Zeckendorf-Wythoff Array Applied to Counting the Number of Representations of N as Sums of Distinct Fibonacci Numbers; M. Bicknell-Johnson. Composing with Sequences: ...Cut is it Art? J.A. Biles. Invariants for Linear Recurrences; M. Caragiu, W. Webb. Base 10 Rats Cycles and Arbitrarily Long Base 10 Rats Cycles; C. Cooper, R.E. Kennedy. Quintics x5 - 5x - k, the Golden Section, and Square Lucas Numbers; M. Elia, P. Filipponi. The Pascal-De Moivre Moments and their Generating Functions; L. Ericksen. Investigating Special Binary Sequences with some Computer Help; D.C. Fielder, C.O. Alford. Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials; P. Filipponi, A.F. Horadam. A Property of the Unit Digits of Recursive Sequences; H.T. Freitag, et al. On General Divisibility of Sums of Integral Powers of the Golden Ratio; H.T. Freitag, D.C. Fielder. Sylvester's Algorithm and Fibonacci Numbers; H.T. Freitag, G.M. Phillips. On the Characteristic Polynomial of the J-TH Order Fibonacci Sequence; G.W. Grossman and S.K. Narayan. Quasi Morgan-Voyce Polynomials and Pell Convolutions; A.F. Horadam. On a Symptotic Maximality of the Fibonacci Tree; Y. Horibe. Generalizations of a Fibonacci Identity; F.T. Howard. Some Generalizations of Wolstenholme's Theorem; W.A. Kimball and W.A. Webb. Card Sorting Related to Fibonacci Numbers; C. Kimberling. On the Inhomogeneous Geometric Line-Sequence; J. Lee. Fibonacci Numbers of the Form k2 + k + 2; F. Luca. On Certain Polynomials of Even Subscripted Lucas Numbers; R.S. Melham. On the Rank of Appearance of Lucas Sequences; S. Müller. Algorithmic Simplification of Reciprocal Sums; S. Rabinowitz. Solved and Unsolved Problems on Pseudoprime Numbers and their Generalizations; A. Rotkiewicz. Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials; A.G. Shannon, A.F. Horadam. Special Multipliers of Lucas Sequences Modulo pr; L. Somer. Digital Halftoning Using Error Diffusion and Linear Pixel Shuffling; J. Szybist and P.G. Anderson. On Vector Sequence Recurrence Equations in Fibonacci Vector Geometry; J.C. Turner. Constructing Identities Involving Kth-Order F-L Numbers by using The Characteristic Polynomial; C. Zhou. Subject Index.