Consider a Cartesian grid, with verteces at integer x and y values, where every four vertices around a vacant space define a unit square. An Aztec Diamond of order d is the shape formed by all unit squares whose centers satisfy the equation:
abs(x) + abs(y) <= d
Given the order of an Aztec Diamond, d (positive integer), return the number, n, of possible tilings using domino tiles, i.e. rectangles sized 1x2 and 2x1, such that:
An Aztec Diamond of order 4 is shown at this URL.
Input: d = 4
Output: n = 1024