@Placholdr you can write a Fibbonacci function like that but it's not very efficient, because you end up calculating the ancestor values many more times than is necessary.

The underlying structure of the Fibonacci sequence isn't tree recursive because F(n) = F(n-1) + F(n-2), but F(n-1) is itself dependent on F(n-2). So if the two branches of your tree are F(n-1) and F(n-2), you have a duplicate copy of the F(n-2) subtree embedded in the F(n-1) subtree. This compounds at each level so for large n you'll have a very large tree but most of it will just be copies of various parts of itself.

In many cases a lookup table is the best way to go. Even if you need the full range of 64-bit unsigned integers, there's still fewer than a hundred entries in your table.