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Nice. When I was a teenage self-taught programmer, an article like this one, but about the superiority of quicksort to insertion sort, was the trigger that got me to understand that thinking mathematically about algorithms could lead us to a kind of understanding that transcended mere coding (although I couldn't have put it in those words at that time). It was quite an epiphany.

I can imagine, today, a young enthusiast having learned Python and maybe done a few Project Euler exercises, stumbling upon that post and being amazed that you could generate Fibonacci numbers that way, and thinking that maybe there is something interesting about that "generating functions" thing.

If that's you reading this, it's dangerous to go alone. Take this: https://www.math.upenn.edu/~wilf/DownldGF.html

And then after Wilf, read Flajolet and Sedgewick: http://algo.inria.fr/flajolet/Publications/book.pdf

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