Consider a binary tree with n nodes. How many different possible binary trees structures are there?
I tried something like:
n number of different structure:
1 1
2 4
3 16
so is that 4(n-1) for n >1 ; 1 for n == 1?
The number of different binary trees that can be formed using n nodes is given by the nth Catalan number.
number of nodes (n) binary trees C(n)
1 1
2 2
3 5
4 14
See:
http://en.wikipedia.org/wiki/Binary_tree
http://en.wikipedia.org/wiki/Catalan_number