Recursive function (idea)

And now, for your excitement, the Fibonacci sequence:
f(n) = f(n-1) + f(n-2); f(0) = f(1) = 1.

While we're at it, here's a nifty sequence from Gödel, Escher, Bach: An Eternal Golden Braid:
g(n)=n-g(g(n-1)); g(0)=0.

Whee. . .. ... ..... ........ ............. .................... ..................................