A(X) = U(X,X)
U(X,Y) = X + U(X2 + 2XY, X)
But I can't figure out exactly why. Certainly I have a clue as to why the X2 + 2XY is in there, since it must correspond to the fact that an AVL tree of height h is made out of two such trees each of height h-1, or one tree of height h-1 and one of h-2. So I nearly grasp that X stands for AVL-tree-of-height-h-1 and Y is AVL-tree-of-height-h-2, but somehow I can't make everything else line up right. Unfortunately the cited article that explains the whole story is (a) in a library not open on the weekends, and (b) (it should be noted this is a much more permanent problem) very probably in French.
Today was actually productive since