Motzkin Paths of Bounded Height with Two Forbidden Contiguous Subwords of Length Two
Helmut Prodinger
Department of Mathematics
University of Stellenbosch
7602 Stellenbosch
South Africa
and
NITheCS (National Institute for Theoretical and Computational Sciences)
South Africa
Abstract:
We revisit the topic of Motzkin excursions and meanders, which we
consider in the context of forbidden patterns. We continue previous work
of Asinowski, Banderier, Gittenberger, and Roitner, leading to matrix
equations and also continued fractions. The enumeration is done by
properly setting up bivariate generating functions that can be expanded
using the kernel method.
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(Concerned with sequences
A004149
A023431
A217282
A308435
A329666
A329667
A329668
A329669
A329675
A329676
A329701
A329702.)
Received November 13 2023; revised versions received November 1 2025; December 7 2025;
December 8 2025.
Published in Journal of Integer Sequences,
December 8 2025.
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