|Journal of Integer Sequences, Vol. 8 (2005), Article 05.1.6|
Abstract: We consider those lattice paths that use the steps Up, Level, and Down with assigned weights w, u, and v. In probability theory, the total weight is 1. In combinatorics, we regard weight as the number of colors and normalize by setting w=1. The lattice paths generate Motzkin sequences. Here we give a combinatorial proof of a three-term recursion for a weighted Motzkin sequence and we find the radius of convergence.
(Concerned with sequences A000108 A001003 and A001006 .)
Received January 9 2005; revised version received February 24 2005. Published in Journal of Integer Sequences February 28 2005.