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This is pretty close to Knuth's discussion of Fibonacci Numbers in TAOCP. I'm inclined that's where this came from, and that this is missing an attribution.

In either case, if you enjoyed this post add one to the "I-should-read-TAOCP" (or "I-should-continue-reading-TAOCP") tally. I did...

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Knuth is great, but if we are going to attribute this derivation, we have to go far longer back in time. De Moivre was the first to derive a closed formula for the Fibonacci numbers, and he did so by "inventing" generating functions. I only have wikipedia as a source right now, as I have most of my math books, including the few on the history of mathematics I have, in boxes :)

http://en.wikipedia.org/wiki/History_of_combinatorics

OP here, I have actually not read TAOCP at all. It's just a derivation I sometimes use to pass a few minutes while waiting/bored and I thought I'd blog about it.

Yeah, sorry, I stand corrected.

No problem.

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