Journal of Integer Sequences, Vol. 24 (2021), Article 21.4.1

A Matrix Approach to Generalized Delannoy and Schröder Arrays

Luis Verde-Star
Department of Mathematics
Universidad Autónoma Metropolitana
Apartado 55–534, CdMx, 09340


We construct a set of Pascal-like infinite matrices that contains the generalized Delannoy arrays associated with weighted lattice paths. From each of our Delannoy matrices we obtain several Schröder arrays. We construct the matrices combining two Pascal translation matrices and a diagonal matrix, and we find explicit formulas for the entries of the matrices, and recurrence relations and generating functions for the central generalized Delannoy and Schröder numbers. We also express the entries of all the generalized Delannoy matrices in terms of Jacobi polynomials.

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(Concerned with sequences A000262 A000326 A002412 A002418 A002720 A006319 A008288 A009766 A033877 A047891 A049600 A051843 A052852 A062147 A062266 A103210 A110190 A151374 A268208.)

Received August 15 2020; revised version received March 4 2021; March 5 2021; March 6 2021; March 12 2021. Published in Journal of Integer Sequences, March 12 2021.

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