Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences
Combinatorics
2007-05-23 v1
Abstract
In this paper we find closed form for the generating function of powers of any non-degenerate second-order recurrence sequence, completing a study begun by Carlitz and Riordan in 1962. Moreover, we generalize a theorem of Horadam on partial sums involving such sequences. Also, we find closed forms for weighted (by binomial coefficients) partial sums of powers of any non-degenerate second-order recurrence sequences. As corollaries we give some known and seemingly unknown identities and derive some very interesting congruence relations involving Fibonacci and Lucas sequences.
Cite
@article{arxiv.math/0010149,
title = {Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences},
author = {Pantelimon Stanica},
journal= {arXiv preprint arXiv:math/0010149},
year = {2007}
}
Comments
15 pages