Preprint Article Version 1 This version is not peer-reviewed

# 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

Journal reference: AIMS Mathematics 2020, 5, 1333-1345
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.

## Subject Areas

explicit formula; recursive formula; generalized Motzkin number; Motzkin number; restricted hexagonal number; Catalan number; generating function

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