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

Authors : Elif TAN, Ho Hon LEUNG

Pages : 2084-2093

Doi:10.15672/hujms.539587

View : 18 | Download : 7

Publication Date : 2020-12-08

Article Type : Research Paper

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