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arXiv · 2406.16394

Dyck Paths Enumerated by the Q-bonacci Numbers

Elena Barcucci·Antonio Bernini·Stefano Bilotta·Renzo Pinzani
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Abstract

We consider Dyck paths having height at most two with some constraints on the number of consecutive valleys at height one which must be followed by a suitable number of valleys at height zero. We prove that they are enumerated by so-called Q-bonacci numbers (recently introduced by Kirgizov) which generalize the classical q-bonacci numbers in the case where q is a positive rational.

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Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani. 2024-06-24. Dyck Paths Enumerated by the Q-bonacci Numbers. https://doi.org/10.4204/eptcs.403.13

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