|
%I #12 Jul 21 2017 00:34:14
%S 0,0,0,1,0,0,3,16,0,0,6,78,193,0,0,10,228,1548,2080,0,0,15,520,6714,
%T 27768,21121,0,0,21,1020,21280,181032,474288,206896,0,0,28,1806,55395,
%U 807040,4697166,7888608,1979713,0,0,36,2968,125748,2817240,29708800
%N 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).
%F T(n, d) = (n^(2d) - (3n-2)^d) / 2 for n>0, d>0.
%e The table begins:
%e 0 0 0 0 0 ...
%e 0 0 0 0 0 ...
%e 1 16 193 2080 21121 ...
%e 3 78 1548 27768 474288 ...
%e 6 228 6714 181032 4697166 ...
%e 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.
%e The antidiagonals are read from southwest to northeast.
%Y Cf. A000217(n-2) (T(n,1)).
%Y Cf. A061995 (T(n,2)).
%Y Cf. A166540 (T(n,3)).
%K nonn,tabl
%O 1,7
%A _Andrew Woods_, Aug 30 2011
|
