### AIMS Mathematics

2020, Issue 2: 1333-1345. doi: 10.3934/math.2020091
Research article

# Several explicit and recursive formulas for generalized Motzkin numbers

• Received: 06 November 2019 Accepted: 09 January 2020 Published: 20 January 2020
• MSC : Primary: 05A15; Secondary: 05A19, 05A20, 11B37, 11B83, 34A05

• 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.

Citation: Feng Qi, Bai-Ni Guo. Several explicit and recursive formulas for generalized Motzkin numbers[J]. AIMS Mathematics, 2020, 5(2): 1333-1345. doi: 10.3934/math.2020091

### Related Papers:

• 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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