Submitted:
24 March 2017
Posted:
27 March 2017
You are already at the latest version
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
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