Proceedings of the
15th International Conference on Fibonacci Numbers and Their Applications
Institute of Mathematics and Informatics
Eszterházy Károly College, Eger, Hungary
June 25–30, 2012

Edited by Kálmán Liptai, Ferenc Mátyás and Tibor Juhász

ISSN 1787-5021 (Print)
ISSN 1787-6117 (Online)

Editorial Board Sándor Bácsó, Sonja Gorjanc, Tibor Gyimóthy, Miklós Hoffmann, József Holovács, László Kovács, László Kozma, Kálmán Liptai, Florian Luca, Giuseppe Mastroianni, Ferenc Mátyás, Ákos Pintér, Miklós Rontó, László Szalay, János Sztrik, Gary Walsh Technical Editor Tibor Tómács

Content

Sierpinski-like triangle-patterns in Bi- and Fibo-nomial triangles
by Antal Bege, Zoltán Kátai
Pages: 5–12

Tiling approach to obtain identities for generalized Fibonacci and Lucas numbers
by Hacène Belbachir, Amine Belkhir
Pages: 13–17

On factors of sums of consecutive Fibonacci and Lucas numbers
by Zvonko Tomislav Čerin
Pages: 19–25

Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations
by Charles K. Cook, Michael R. Bacon
Pages: 27–39

Identities in the spirit of Ramanujan's amazing identity
by Curtis Niles Cooper
Pages: 41–55

On h-perfect numbers
by Heiko Harborth
Pages: 57–62

Proof of the Tojaaldi sequence conjectures
by Russell Jay Hendel, Thomas J. Barrale, Michael Sluys
Pages: 63–75

Sums of powers of Fibonacci and Lucas polynomials in terms of Fibopolynomials
by Claudio de Jesús Pita Ruiz V.
Pages: 77–97

Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers
by Takao Komatsu, Florian Luca
Pages: 99–105

Algebraic relations with the infinite products generated by Fibonacci numbers
by Takeshi Kurosawa, Yohei Tachiya, Taka-aki Tanaka
Pages: 107–119

On divisibility properties of some differences of Motzkin numbers
by Tamás Lengyel
Pages: 121–136

On the Fibonacci distances of ab, ac and bc
by Florian Luca, László Szalay
Pages: 137–163

Algebraic independence results for the infinite products generated by Fibonacci numbers
by Florian Luca, Yohei Tachiya
Pages: 165–173

Sonification of multiple Fibonacci-related sequences
by Casey Patrick Mongoven
Pages: 175–192

Primary classes of compositions of numbers
by Augustine O. Munagi
Pages: 193–204

On second order non-homogeneous recurrence relation
by Chandrakant Nagnath Phadte, Shardchandra P. Pethe
Pages: 205–210

Some aspects of Fibonacci polynomial congruences
by Anthony G. Shannon, Charles K. Cook, Rebecca A. Hillman
Pages: 211–217

The On-Line Encyclopedia of Integer Sequences
by Neil J. A. Sloane
Pages: 219–234

A representation of the natural numbers by means of cycle-numbers, with consequences in number theory
by John C. Turner, William J. Rogers
Pages: 235–254

Bridges between different known integer sequences
by Roman Wituła, Damian Słota, Edyta Hetmaniok
Pages: 255–263

When do the Fibonacci invertible classes modulo M form a subgroup?
by Florian Luca, Pantelimon Stănică, Aynur Yalçiner
Pages: 265–270

Problem proposals
by Clark Kimberling
Pages: 271–274