Motzkin numbers of higher rank: Generating function and explicit expression
Toufik Mansour, Matthias Schork, Yidong Sun
TL;DR
This paper derives the generating function and explicit formulas for higher-rank Motzkin numbers, extending known results for the classical case and providing recursion relations for the rank one case.
Contribution
It introduces a generating function and explicit expressions for higher-rank Motzkin numbers, generalizing previous results for the classical Motzkin numbers.
Findings
Derived generating function for higher-rank Motzkin numbers
Obtained explicit formulas for these numbers
Established recursion relations for rank one case
Abstract
The generating function and an explicit expression is derived for the (colored) Motzkin numbers of higher rank introduced recently. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Mathematical Dynamics and Fractals