Preprint Article Version 1 This version is not peer-reviewed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)

How to cite: Qi, F.; Guo, B. Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers. Preprints 2017, 2017030200 (doi: 10.20944/preprints201703.0200.v1). Qi, F.; Guo, B. Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers. Preprints 2017, 2017030200 (doi: 10.20944/preprints201703.0200.v1).

## 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