##
**
A Recursive Relation for Weighted Motzkin Sequences
**

###
Wen-jin Woan

Department of Mathematics

Howard University

Washington, D.C. 20059

USA

**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.

**
Full version: pdf,
dvi,
ps,
latex
**

(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.

Return to
**Journal of Integer Sequences home page**