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arXiv · 2501.06512

A Study of Second-Order Linear Recurrence Sequences via Continuants

Hongshen Chua
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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.

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Hongshen Chua. 2025-01-11. A Study of Second-Order Linear Recurrence Sequences via Continuants. https://arxiv.org/abs/2501.06512

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