Arithmetic into geometric progressions through Riordan arrays

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• 作者：Donatella Merlini ; ^{donatella.merlini@unifi.it} ; Renzo Sprugnoli ^{renzo.sprugnoli@unifi.it}
• 关键词：Arithmetic and geometric progressions ; Lattice paths ; Riordan arrays
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 February 2017
• 年：2017
• 卷：340
• 期：2
• 页码：160-174
• 全文大小：559 K
• 卷排序：340

文摘

In this paper, by using Riordan arrays and a particular model of lattice paths, we are able to generalize in several ways an identity proposed by Lou Shapiro by giving both an algebraic and a combinatorial proof. The identities studied in this paper allow us to move from an arithmetic progression, and other C-finite sequences, to a geometric progression in terms of Riordan array transformations and vice versa, via the Riordan array inverse.