Partial sums and generating functions of products of Horadam numbers with indices in arithmetic progression

Kunle Adegoke

Published 2019-04-13Version 1

The sums $\sum_{j = 0}^k {w_{rj + s} u_{mj + n} z^j }$, $\sum_{j = 0}^k {w_{rj + s} v_{mj + n} z^j }$ and $\sum_{j = 0}^k {w_{rj + s} w_{mj + n} z^j }$ are evaluated; where $r$, $s$, $k$, $m$ and $n$ are arbitrary integers, $z$ is arbitrary, $(w_i)$ is the Horadam sequence; and $(u_i)$ and $(v_i)$ are the Lucas sequences of the first kind, and of the second kind, respectively.