Several explicit and recursive formulas for generalized Motzkin numbers

In the paper, the authors find two explicit formulas and recover a recursive formula for 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.

Bibliographic Details
Main Authors:	Feng Qi, Bai-Ni Guo
Format:	Article
Language:	English
Published:	AIMS Press 2020-01-01
Series:	AIMS Mathematics
Subjects:	explicit formula recursive formula generalized motzkin number motzkin number restricted hexagonal number catalan number generating function
Online Access:	https://www.aimspress.com/article/10.3934/math.2020091/fulltext.html

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spelling	doaj-4afb5904384b415fb17a2dc162efa8872020-11-25T02:56:42ZengAIMS PressAIMS Mathematics2473-69882020-01-01521333134510.3934/math.2020091Several explicit and recursive formulas for generalized Motzkin numbersFeng Qi0Bai-Ni Guo11 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China 2 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China 3 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China3 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, ChinaIn the paper, the authors find two explicit formulas and recover a recursive formula for 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.https://www.aimspress.com/article/10.3934/math.2020091/fulltext.htmlexplicit formularecursive formulageneralized motzkin numbermotzkin numberrestricted hexagonal numbercatalan numbergenerating function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Feng Qi Bai-Ni Guo
spellingShingle	Feng Qi Bai-Ni Guo Several explicit and recursive formulas for generalized Motzkin numbers AIMS Mathematics explicit formula recursive formula generalized motzkin number motzkin number restricted hexagonal number catalan number generating function
author_facet	Feng Qi Bai-Ni Guo
author_sort	Feng Qi
title	Several explicit and recursive formulas for generalized Motzkin numbers
title_short	Several explicit and recursive formulas for generalized Motzkin numbers
title_full	Several explicit and recursive formulas for generalized Motzkin numbers
title_fullStr	Several explicit and recursive formulas for generalized Motzkin numbers
title_full_unstemmed	Several explicit and recursive formulas for generalized Motzkin numbers
title_sort	several explicit and recursive formulas for generalized motzkin numbers
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2020-01-01
description	In the paper, the authors find two explicit formulas and recover a recursive formula for 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.
topic	explicit formula recursive formula generalized motzkin number motzkin number restricted hexagonal number catalan number generating function
url	https://www.aimspress.com/article/10.3934/math.2020091/fulltext.html
work_keys_str_mv	AT fengqi severalexplicitandrecursiveformulasforgeneralizedmotzkinnumbers AT bainiguo severalexplicitandrecursiveformulasforgeneralizedmotzkinnumbers
_version_	1724712696811618304

Several explicit and recursive formulas for generalized Motzkin numbers

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