A194604 Square table T(n, d) read by antidiagonals: number of ways to place 2 nonattacking kings on an n^d (n X n X ...) raumschach board (hypercubical chessboard).

0, 0, 0, 1, 0, 0, 3, 16, 0, 0, 6, 78, 193, 0, 0, 10, 228, 1548, 2080, 0, 0, 15, 520, 6714, 27768, 21121, 0, 0, 21, 1020, 21280, 181032, 474288, 206896, 0, 0, 28, 1806, 55395, 807040, 4697166, 7888608, 1979713, 0, 0, 36, 2968, 125748, 2817240, 29708800

Offset: 1

Author

Andrew Woods, Aug 30 2011

Keywords

• nonn
• tabl

Examples

			The table begins:
0   0    0      0       0 ...
0   0    0      0       0 ...
1  16  193   2080   21121 ...
3  78 1548  27768  474288 ...
6 228 6714 181032 4697166 ...
There are T(3, 4) = 2080 ways to place 2 nonattacking kings on a 3^4 (3 X 3 X 3 X 3) hypercubical chessboard.
The antidiagonals are read from southwest to northeast.
		

Crossrefs

Cf. A000217(n-2) (T(n,1)).

Cf. A061995 (T(n,2)).

Cf. A166540 (T(n,3)).

Formula

T(n, d) = (n^(2d) - (3n-2)^d) / 2 for n>0, d>0.