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 left bracketing bar x - 1/2 right bracketing bar + left bracketing bar y - 1/2 right bracketing bar <=n. The first few are illustrated above. The number of squares in the Aztec diamond of order n is 2n(n + 1), giving for n = 1, 2, ... the values 4, 12, 24, 40, 60, ... (OEIS A046092).

centered square number | diamond | triangular number