GCD properties in Hosoya's triangle
type: Item
instance of: scholarly article
zbMATH Open document ID: 1271.11016
author: Rigoberto Flórez
author: Leandro Junes
publication date: 2012-06-29T00:00:00Z
full work available at URL: florez.pdf
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 6051051
zbMATH Keywords: recurrence
zbMATH Keywords: Hosoya sequence
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: Pascal triangle
zbMATH Keywords: polygon
zbMATH Keywords: Star of David
zbMATH Keywords: rhombus
zbMATH Keywords: greatest common divisor
MaRDI profile type: Publication
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title: GCD properties in Hosoya's triangle
published in: The Fibonacci Quarterly
review text: The Hosoya sequence \(H(r, k)\) is defined by the recurrences \(H(r, k)=H(r-1, k)+H(r-2, k)\) and \(H(r, k)=H(r-1, k-1)+H(r-2, k-2)\) with certain initial coditions, (see \textit{H. Hosoya} [Fibonacci Q. 14, 173--179 (1976; Zbl 0359.10011)]). Hosoya proved that \(H(k, r)=F_{k}F_{r-k+1}\), where \(F_n\) is the Fibonacci sequence. The Hosoya sequence gives rise to the Hosoya triangle, analogous to the Pascal triangle.NEWLINENEWLINEThe present authors prove GCD properties for numbers in the Star of David and other polygon configurations formed in the Hosoya triangle. They also give a criterion to determine whether a sequence of points in a polygon or in a rhombus configurations in the Hosoya triangle have GCD equal to one. Several known results from the Pascal triangle are transferred to the Hosoya triangle.
reviewed by: Pentti Haukkanen
description: scientific article; zbMATH DE number 6051051