A note on sum of k-th power of Horadam's sequence

Details A note on sum of k-th power of Horadam's sequence A note on sum of k-th power of Horadam's sequence

2003-02-02

arxiv.org/abs/math/0302015v1

Mathematics

Combinatorics

5 pages

Scientific paper

Let $w_{n+2}=pw_{n+1}+qw_{n}$ for $n\geq0$ with $w_0=a$ and $w_1=b$. In this
paper we find an explicit expression, in terms of determinants, for
$\sum_{n\geq0} w_n^kx^n$ for any $k\geq1$. As a consequence, we derive all the
previously known results for this kind of problems, as well as many new
results.

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