I've written about convolutions before in two posts:
- A Practical Example of a Convolution on the 12th of October 2025
- Convolutions Revisited on the 1st May 2026
- Cartesian Product versus Self-Convolution on the 1st of May 2026
Today, having turned 28347 days old, I noticed that this number is a member of OEIS A023609:
A023609: convolution of Fibonacci numbers and composite numbers.
Here an explanation from Gemini about how this sequence is generated (link) as well as code and visualisations. In future, it's probably better to just post Gemini links rather than copying and pasting because this seems to always incur formatting problems.
Just a reminder that in integer sequences, a convolution combines two sequences, $A$ and $B$, to produce a third sequence. The $n$-th term of the new sequence is calculated by taking the first $n$ terms of $A$ and the first $n$ terms of $B$, reversing the order of $B$, multiplying the aligned pairs, and summing the results.
Here we have A = 1, 1, 2, 3, 5, 8, 13, 21... and B = 4, 6, 8, 9, 10, 12, 14, 15... and thus we get:
- first term is A(1) x B(1) = 1 x 4 = 4
- second term is A(1) x B(2) + A(2) x B(1) = 1 x 6 + 4 x 1 = 10
- third term is A(1) x B(3) + A(3) x B(1) + A(2) x B(2) = 1 x 8 + 2 x 4 + 1 x 6 = 22
The sequence begins:
4, 10, 22, 41, 73, 126, 213, 354, 583, 955, 1558, 2534, 4114, 6672, 10811, 17509, 28347, 45884, 74261, 120177, 194471, 314682, 509188, 823906, 1333132, 2157077, 3490249, 5647368, 9137661
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