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https://mathworld.wolfram.com/AztecDiamond.html

An Aztec diamond of order n is the region obtained from four staircase shapes of
height n by gluing them together along the straight edges.

It can therefore be defined as the union of unit squares in the plane whose edges lie
on the lines of a square grid and whose centers (x,y) satisfy

|x-1/2|+|y-1/2|<=n.