Wilf's "Snake Oil" Method Proves an Identity in The Motzkin Triangle

TL;DR

This paper demonstrates the application of Herb Wilf's Snake Oil Method to prove a specific identity within the Motzkin Triangle, showcasing its utility in combinatorial enumeration problems.

Contribution

It provides a new proof of a Motzkin Triangle identity using Wilf's Snake Oil Method, illustrating its broader applicability to general triangles.

Findings

Successfully proves a Motzkin Triangle identity

Shows the method's potential for other combinatorial identities

Highlights the method's versatility in triangle-based enumeration

Abstract

We give yet-another illustration of using Herb Wilf's Snake Oil Method, by proving a certain identity between the entries of the so-called Motzkin Triangle, that arose in a recent study of enumeration of certain classes of integer partitions. We also briefly illustrate how this method can be applied to general `triangles'.