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math.CO2026
Motzkin paths with two variants of level steps on odd levels -- a kernel method approach
Helmut Prodinger
The sequence A176677 in the Encyclopedia of Integer Sequences enumerates Motzkin paths where two types of horizontal steps may occur, but only on odd indexed levels. We show how to…
math.CO2026
Pell-Padovan tetranacci numbers and their Hadamard product with classical sequences
Helmut Prodinger
A quick way to compute generating functions related to Pell-Padovan tetranacci numbers and classical sequences of recursions of order two is provided. Eight special instances can b…
math.CO2026
Ordered trees with distinguished children
Helmut Prodinger
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of…