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

1,7

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

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)).

Sequence in context: A364799 A004002 A216149 * A078355 A107823 A139815

Adjacent sequences: A194601 A194602 A194603 * A194605 A194606 A194607

Keyword

nonn,tabl

Author

Andrew Woods, Aug 30 2011

Status

approved