A Study of Second-Order Linear Recurrence Sequences via Continuants
Number Theory
2025-08-26 v1
Abstract
This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet formula for continuants. Using this result, we provide a continuant-based formulation for well-known identities associated with Lucas sequences.
Cite
@article{arxiv.2501.06512,
title = {A Study of Second-Order Linear Recurrence Sequences via Continuants},
author = {Hongshen Chua},
journal= {arXiv preprint arXiv:2501.06512},
year = {2025}
}
Comments
Journal of Integer Sequences (2023)