English

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.

Keywords

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}
}
R2 v1 2026-06-28T07:32:43.992Z