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

Matthias Schork
Camillo-Sitte-Weg 25
60488 Frankfurt

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


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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