Journal of Integer Sequences, Vol. 28 (2025), Article 25.7.6

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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