An Aztec diamond of order 
is the region obtained from four staircase shapes of height 
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 
satisfy
 |
The first few are illustrated above. The number of squares in the Aztec diamond of order 
is 
, giving for 
, 2, ... the values 4, 12, 24, 40, 60, ... (OEIS A046092).
The number of domino tilings of an order 
Aztec diamond is 
, where 
is the triangular number 
(Elkies et al. 1992).
Note that Wassermann appears to use an incorrect definition of the Aztec diamond that is actually equivalent to that of a centered square number.
