title: why AVL tree max height given N is 1.44log(N+2)-1.328
body: <p>we know that in worst case <code>S(h)=S(h-1)+S(h-2)+1</code>,I've also seen <a href="https://stackoverflow.com/questions/30769383/finding-the-minimum-and-maximum-height-in-a-avl-tree-given-a-number-of-nodes">Evan Bechtol's answer</a>,but there's no obvious deduction there. How to get the <a href="https://i.stack.imgur.com/sgX19.png" rel="nofollow noreferrer">formula</a>      from<code>S(h)=S(h-1)+S(h-2)+1</code>?</p>