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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.

Keywords

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)

R2 v1 2026-06-28T21:03:25.879Z