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Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers
Version 1
: Received: 24 March 2017 / Approved: 27 March 2017 / Online: 27 March 2017 (11:02:41 CEST)
A peer-reviewed article of this Preprint also exists.
Feng Qi and Bai-Ni Guo, Several explicit and recursive formulas for generalized Motzkin numbers. AIMS Mathematics. 2020, 5, doi:10.3934/math.2020091 Feng Qi and Bai-Ni Guo, Several explicit and recursive formulas for generalized Motzkin numbers. AIMS Mathematics. 2020, 5, doi:10.3934/math.2020091
Abstract
In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.
Keywords
explicit formula; recursive formula; generalized Motzkin number; Motzkin number; restricted hexagonal number; Catalan number; generating function
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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