The nth number of the fibonacci sequence is defined as F(n) = F(n-1) + F(n-2) for n > 1, and n for n <= 1.

This is a recursive definition, i.e. the result of F(n) depends on itself.^{1}

Then some guy, Jacques Philippe Marie Binet, did something cool. He, through some mathematical wizardry, found the ‘explicit’ formula, i.e. non-recursive. And it goes like this:

Unless n is less than or equal to 1. ↩