A formula for the generating functions of powers of Horadam's sequence

@article{Mansour2004AFF,
title={A formula for the generating functions of powers of Horadam's sequence},
author={Toufik Mansour},
journal={Australasian J. Combinatorics},
year={2004},
volume={30},
pages={207-212}
}

The second-order linear recurrence sequence (wn(a, b; p, q))n≥0, or briefly (wn)n≥0, is defined by wn+2 = pwn+1 + qwn, (1) with w0 = a, w1 = b and n ≥ 0. This sequence was introduced in 1965 by Horadam [3, 4], and it generalizes many sequences (see [1, 5]). Examples of such sequences are Fibonacci number sequences (Fn)n≥0, Lucas number sequences (Ln)n≥0, and Pell number sequences (Pn)n≥0, when one has p = q = b = 1, a = 0; p = q = b = 1, a = 2; and p = 2, q = b = 1, a = 0; respectively. In this… CONTINUE READING