The problem of determining how many nonattacking kings can be placed on an 
chessboard. For 
, the solution is 16, as illustrated
above (Madachy 1979). In general, the solutions are
 |
(1)
|
(Madachy 1979), giving the sequence of doubled squares 1, 1, 4, 4, 9, 9, 16, 16, ... (OEIS A008794). This sequence has generating function
 |
(2)
|
The minimal number of kings needed to occupy or attack every square on an 
chessboard (i.e., domination numbers for the 
king graphs) are given
for 
, 2, ... by 1, 1, 1, 4, 4, 4, 9, 9,
9, 16, ... (OEIS A075561), with the 
case illustrated above and noted by (Madachy
1979, p. 39). In general, for an 
chessboard,
 |
(3)
|
