By Shalosh B. Ekhad and Doron Zeilberger
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.
the input file yields the output file
the input file yields the output file