  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.

Combinatorics