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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
Keywords:
lattice paths
Software:
OEIS
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