A Study of Second-Order Linear Recurrence Sequences via Continuants

2025/01/11 by Chua, Hongshen
#11A55 (Primary) #11B39 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.06512

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.

Related

• An Identity for Second Order Sequences Obeying the Same Recurrence Relation
• Identities for second order recurrence sequences
• Continuants and convergence of certain continued fractions
• Combinatorics of Continuants of Continued Fractions with 3 Limits
• Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials