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.
Arithmetic into geometric progressions through Riordan arrays / D. Merlini; R. Sprugnoli. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 340:(2017), pp. 160-174. [10.1016/j.disc.2016.08.017]
Arithmetic into geometric progressions through Riordan arrays
MERLINI, DONATELLA;SPRUGNOLI, RENZO
2017
Abstract
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.File | Dimensione | Formato | |
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