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.