For extra points, check out what Wikipedia has to say about Fibonacci numbers, and then implement a recursive1 solution.
Recursion can lead to some wonderfully beautiful solutions to programming problems, but not always efficiently. Memoize can often increase their efficiency greatly, so take a look at that too.
Post your solutions here for further comment, and enjoy your journey.
Good luck
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[1] 30 years ago, when I was a student, one of the researchers told me about quicksort. He told me that to sort a list, I should split it in to two lists, sort each list, and repeat. That was when I recognised the beauty of recursion.
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