Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers

Feng Qi; Bai-Ni Guo

doi:10.20944/preprints201703.0200.v1

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

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

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.

Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers

Abstract

Keywords

Subject

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