What is your favorite fibs?
I can't decide between memoized recursive fibs and dynamic programming fibs. I'd use the first if I have to call it often (at the cost of higher space costs) and the second if I don't have to call it as often, or space costs are considered unacceptable.
I've needed fibs in a real program exactly once. I needed to determine the maximum number of leaves (for visualization) in a level of a certain kind of tree under certain constraints I've since then forgotten, and it turned out that the sequence was indeed the fibonacci one. I don't remember how I ended up calculating it, but it wouldn't have made much difference since the maximum depth was around twenty and the function was called very rarely.