Identities for full-history Horadam sequences
Combinatorics
2022-12-14 v1
Abstract
We prove a master identity for a class of sequences defined by full-history linear homogeneous recurrences with (non-negative) constant coefficients. The identity is derived in a combinatorial way, providing thus combinatorial proofs for many known and new identities obtained as its corollaries. In particular, we prove several interesting identities for the Pell, the Jacobsthal, and the m-nacci numbers.
Cite
@article{arxiv.2212.06734,
title = {Identities for full-history Horadam sequences},
author = {Tomislav Došlić and Luka Podrug},
journal= {arXiv preprint arXiv:2212.06734},
year = {2022}
}