A note on congruence properties of the generalized bi-periodic Horadam sequence

Year 2020, Volume: 49 Issue: 6, 2084 - 2093, 08.12.2020

Elif Tan , Ho Hon Leung

https://doi.org/10.15672/hujms.539587

Cited By: 3

Abstract

In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.

Keywords

Horadam sequence, generalized Fibonacci sequence, generalized Lucas sequence, congruence

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