Automatic Generation of Convolution Identities for C-finite sequences
Combinatorics
2021-08-09 v1
Abstract
In a recent insightful article, Helmut Prodinger uses sophisticated complex analysis, with residues, to derive convolution identities for Fibonacci, Tribonacci, and k-bonacci numbers. Here we use a naive, "experimental mathematics" (yet fully rogorous!) approach, using the C-finite ansatz, that can derive such identities in a few seconds, but not just for the above-mentioned sequences, but for every C-finite sequence (i.e. a sequence satisfying a linear recurrence with constant coefficients), and even for a pair of these.
Cite
@article{arxiv.2108.02918,
title = {Automatic Generation of Convolution Identities for C-finite sequences},
author = {Shalosh B. Ekhad and Doron Zeilberger},
journal= {arXiv preprint arXiv:2108.02918},
year = {2021}
}
Comments
3 pages. Accompanied by a Maple package and output files available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/prodinger.html