4 papers
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…
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…
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…
Cornerless, peakless, valleyless Motzkin paths (regular and skew) and applications to bargraphs
Helmut Prodinger
Motzkin paths consist of up-steps, down-steps, horizontal steps, never go below the -axis and return to the -axis. Versions where the return to the -axis isn't required ar…