Journal of Integer Sequences, Vol. 17 (2014), Article 14.3.6

GCD Property of the Generalized Star of David in the Generalized Hosoya Triangle


Rigoberto Flórez
Department of Mathematics and Computer Science
The Citadel
Charleston, SC 29409
USA

Robinson A. Higuita
Departamento de Matemáticas
Universidad de Antioquia
Medellín
Colombia

Leandro Junes
Department of Mathematics, Computer Science and Information Systems
California University of Pennsylvania
California, PA 15419
USA

Abstract:

The generalized Hosoya triangle is an arrangement of numbers in which each entry is a product of two generalized Fibonacci numbers. We prove the GCD property for the star of David of length two. We give necessary and sufficient conditions such that the star of David of length three satisfies the GCD property. We propose some open questions and a conjecture for the star of David of length bigger than or equal to four. We also study GCD properties and modularity properties of generalized Fibonacci numbers.


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(Concerned with sequences A000032 A000045.)


Received August 22 2013; revised versions received December 11 2013; January 28 2013. Published in Journal of Integer Sequences, February 16 2014.


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