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A recursive relation for weighted Motzkin sequences. (English) Zbl 1065.05012
Summary: 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.

##### MSC:
 05A15 Exact enumeration problems, generating functions 05A19 Combinatorial identities, bijective combinatorics
lattice paths
OEIS
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