• Corpus ID: 118172952

# Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences

@article{Stnic2000GeneratingFW,
title={Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences},
author={Pantelimon Stănică},
journal={arXiv: Combinatorics},
year={2000}
}
• P. Stănică
• Published 15 October 2000
• Mathematics
• arXiv: Combinatorics
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…
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