A easy to read python solution

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    The basic concept is that we keep judging if the left child sub-tree of a node is a fully grown BST. If then, we count the num of elements of the last layer and recursively examine its right sub-tree. Or we directly examine its left sub-tree. The time comsumption is O(h^2), that is O(lg^2n)

       class Solution:
            # @param {TreeNode} root
            # @return {integer}
            def getTreeHeight(self, root):
                Return the height of a BST
                height = 0
                    height += 1
                    root = root.left
                return height
        def countNodes(self, root):
            height = self.getTreeHeight(root)
            count = 0  # We use count to count the elements in the last layer
            for i in xrange(1,height):
                # If the left child tree is a fully-grown BST
                if self.getTreeHeight(root.right) == height - i:
                    count += 2 ** (height - 1 - i)
                    root = root.right
                    root = root.left
            # Plus the upper h-1 layers of nodes
            return count + 2 ** (height-1)

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