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arXiv · 2607.22955

Holonomic Sequences Arising from Laplace Transforms of Generalized Second Order Sequences

Rigoberto Flórez·Robinson Higuita-Diaz·José L. Ram\'ırez
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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.

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Rigoberto Flórez, Robinson Higuita-Diaz, José L. Ram\'ırez. 2026-07-24. Holonomic Sequences Arising from Laplace Transforms of Generalized Second Order Sequences. https://arxiv.org/abs/2607.22955

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