The problem of determining how many nonattacking kings can be placed on an n×n chessboard. For n = 8, the solution is 16, as illustrated above. In general, the solutions are K(n) = {1/4 n^2 | n even 1/4 (n + 1)^2 | n odd auto right match (Madachy 1979), giving the sequence of doubled squares 1, 1, 4, 4, 9, 9, 16, 16, ... (OEIS A008794). This sequence has generating function (1 + x^2)/((1 - x^2)^2(1 - x)) = 1 + x + 4x^2 + 4x^3 + 9x^4 + 9x^5 + ....

bishops problem | chess | hard hexagon entropy constant | knights problem | queens problem | rooks problem