Journal of Integer Sequences, Vol. 26 (2023), Article 23.8.8

A Study of Second-Order Linear Recurrence Sequences via Continuants

Hongshen Chua
Puchong 47170


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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(Concerned with sequences A000129 A041011.)

Received August 28 2023; revised versions received October 19 2023; October 20 2023. Published in Journal of Integer Sequences, October 31 2023.

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