Summary: 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.

05A15, 05A19

Motzkin paths, combinatorial identity