Document Type

Article

Publication Date

2018

Publication Source

Journal of Integer Sequences

Abstract

We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, and illustrates an interesting occurrence of the Catalan and generalized Motzkin numbers in a context a priori void of combinatorial objects.

ISBN/ISSN

1530-7638

Document Version

Published Version

Comments

This article is made available with the permission of the author in compliance with the publisher's policy on open access. Permission documentation is on file.

Volume

21

Issue

8

Peer Reviewed

yes

Download

Share

COinS