What is the an upper bound for the height of an AVL tree with N nodes?

This can be determined if we can answer the reverse question:

What is a lower bound for the number of nodes in an AVL tree of height h?

Let f(h) be the minimum number of nodes that can be in an AVL tree of height h.

Then

      f(-1) = 0
      f(0) = 1
      f(1) = 2
   

For h >= 1,