Journal of Integer Sequences, Vol. 10 (2007), Article 07.7.4

Motzkin Numbers of Higher Rank: Generating Function and Explicit Expression


Toufik Mansour
Department of Mathematics
University of Haifa
Haifa 31905
Israel

Matthias Schork
Camillo-Sitte-Weg 25
60488 Frankfurt
Germany

Yidong Sun
Department of Mathematics
Dalian Maritime University
116026 Dalian
P. R. China

Abstract:

The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. C onsidering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.

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(Concerned with sequences A000108, A001006, and A104184 .)

Received April 20 2007; revised version received June 13 2007. Published in Journal of Integer Sequences, July 4 2007.

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