A Combinatorial Proof for the Generating Function of Powers of a Second-Order Recurrence Sequence
Yifan Zhang and George Grossman
Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48858
In this paper, we derive a formula for the generating function of
powers of a second-order linear recurrence sequence, with initial
conditions 0 and 1. As an example, we find the generating function of
the powers of the nonnegative integers. We also find new formulas for
computing Eulerian polynomials.
Full version: pdf,
(Concerned with sequences
Received January 17 2017; revised versions received February 3 2017; November 1 2017; January 21 2018.
Published in Journal of Integer Sequences, March 9 2018.
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