Finding the highest array position needed for linear representation of a Binary Tree

If a binary tree has suppose 9 nodes then array position for storing its highest possible Root is found like this:

9 = 2^3 + 1

So it’s possible maximum Root is 2^3 – 1 = 7.

So it will take 7 x 2 = 14 places to linearly represent that tree.
And if we are to store even the possible NULLs then it takes 14 x 2 + 1 = 29 Places to linearly represent that tree.
It actually corresponds to the 2^d + 1 formula.
See, if 9 is the maximum node then the tree’s depth is actually 4. And the highest node or Root possible at that level is simply 2^d-1.