Journal of Integer Sequences, Vol. 10 (2007), Article 07.9.1

From (2,3)-Motzkin Paths to Schröder Paths

Sherry H. F. Yan
Department of Mathematics
Zhejiang Normal University
Jinhua 321004
P. R. China


In this paper, we provide a bijection between the set of restricted (2,3)-Motzkin paths of length n and the set of Schröder paths of semilength n. Furthermore, we give a one-to-one correspondence between the set of (2,3)-Motzkin paths of length n and the set of little Schröder paths of semilength n+1. By applying the bijections, we get the enumerations of Schröder paths according to the statistics "number of udd's" and "number of hd's".

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(Concerned with sequences A000108 A001003 and A006318 .)

Received June 18 2007; revised version received August 24 2007. Published in Journal of Integer Sequences, August 24 2007.

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