Holonomic Sequences Arising from Laplace Transforms of Generalized Second Order Sequences
Combinatorics
2026-07-24 v1
Abstract
We study the FiboLaplace and LucasLaplace sequences obtained by applying the Laplace transform to generalized Fibonacci-type and Lucas-type polynomials. We relate these families and show that, for each fixed transform parameter, the FiboLaplace sequence is holonomic. We give a combinatorial interpretation in terms of weighted colored tilings, leading to recurrence relations, identities, and a triangular refinement by the number of dominoes. We also derive two continued-fraction expansions and obtain a second combinatorial interpretation in terms of generalized Motzkin paths. These results extend earlier work of Givens and Moll.
Cite
@article{arxiv.2607.22955,
title = {Holonomic Sequences Arising from Laplace Transforms of Generalized Second Order Sequences},
author = {Rigoberto Flórez and Robinson Higuita-Diaz and José L. Ramírez},
journal= {arXiv preprint arXiv:2607.22955},
year = {2026}
}