An Aztec diamond of order , where is a nonnegative integer,
is the region obtained from four staircase shapes of height
by gluing them together along the straight
edges. Order 0 gives the empty region.
It can therefore be defined as the union of unit
squares in the plane whose edges
lie on the lines of a square
grid with integer coordinates 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 dominotilings of an order
Aztec diamond is , where is the triangular number (Elkies et al. 1992, Eu
and Fu 2005). For , there is one empty tiling.
, where 
is a nonnegative integer,
is the region obtained from four staircase shapes of height
by gluing them together along the straight
edges. Order 0 gives the empty region.
It can therefore be defined as the union of unit
squares in the plane whose edges
lie on the lines of a square
grid with integer coordinates and whose centers 
satisfy
is 
, giving for 
, 2, ... the values 4, 12, 24, 40, 60, ... (OEIS A046092).
Aztec diamond is 
, where 
is the triangular number 
(Elkies et al. 1992, Eu
and Fu 2005). For 
, there is one empty tiling.
instead selects 
squares on this square
grid, giving a centered square number.
