• 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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