Dyck Paths Enumerated by the Q-bonacci Numbers
<|reference_start|>Dyck Paths Enumerated by the Q-bonacci Numbers: 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.<|reference_end|>
@article{barcucci2024dyck,
    title={Dyck Paths Enumerated by the Q-bonacci Numbers},
    author={Elena Barcucci (University of Florence), Antonio Bernini (University
  of Florence), Stefano Bilotta (University of Florence), Renzo Pinzani
  (University of Florence)},
    journal={EPTCS 403, 2024, pp. 49-53},
    year={2024},
    doi={10.4204/EPTCS.403.13},
    archivePrefix={arXiv},
    eprint={2406.16394},
    primaryClass={cs.DM math.CO}
}