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

• Prodinger.txt

Sample Input and Output files for Prodinger.txt

• If you want to see an article for the binomial convolution of the k-bonacci numbers with themselves for k from 2 to 20

  the input file yields the output file

• If you want to see an article for the binomial convolution of the a-bonacci numbers b-bonacci numbers for 2 ≤ a ≤ b ≤ 10

  the input file yields the output file

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