Automatic Generation of Convolution Identities for C-finite sequences

By Shalosh B. Ekhad and Doron Zeilberger

.pdf   .tex  

Written: Aug. 5, 2021 .

In this 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.

Maple package

Sample Input and Output files for Prodinger.txt

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