Basic properties of a generalized third order sequence of numbers

Kunle Adegoke

paper

Basic properties of a generalized third order sequence of numbers

arXiv:1906.00788

Abstract

We study the properties of the third order sequence $(w_{n}) = (w_{n} (a, b, c; r, s, t))$ defined by the recurrence relation $w_{n} = r w_{n - 1} + s w_{n - 2} + t w_{n - 3} (n \geq 3)$ with $w_{0} = a, w_{1} = b, w_{2} = c$ , where $a$ , $b$ , $c$ , $r$ , $s$ and $t$ are arbitrary complex numbers and $t \neq = 0$ . Properties examined include the partial sum of the terms of the sequence, with indices in arithmetic progression, as well as double binomial summation identities.

12 pages, no figures