Carol Number

A Carol number is an integer of the form 4ⁿ - 2⁽ⁿ⁺¹⁾ - 1. An equivalent formula is (2ⁿ-1)² - 2.
An Interesting Property : 
For n > 2, the binary representation of the n-th Carol number is n-2 consecutive one's, a single zero in the middle, and n + 1 more consecutive one's. Example, n = 4 carol number is 223 and binary of 223 is 11011111, here n-2 = 4-2 = 2 consecutive ones in starting then single 0 in middle and then n + 1 = 4 + 1 = 5 consecutive ones after it.
Given a number n, the task is to find the nth Carol Number. First, few carol numbers are -1, 7, 47, 223, 959... etc.

Examples : 

Input : n = 2
Output: 7

Input : n = 4
Output: 223

Output : 

223

Time complexity: O(log n) , for pow function

Auxiliary Space: O(1)