|Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.7|
Abstract: We consider those lattice paths that use the steps "up", "level", and "down" with assigned weights w,b,c. In probability theory, the total weight is 1. In combinatorics, we replace weight by the number of colors. Here we give a combinatorial proof of a relation between restricted and unrestricted weighted Motzkin paths.
(Concerned with sequences A000108 and A001003 .)
Received October 4 2005; revised version received January 28 2006. Published in Journal of Integer Sequences January 29 2006.