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%I #40 Apr 27 2019 07:37:15
%S 0,1,4,13,31,66,123,214,346,535,790,1131,1569,2128,2821,3676,4708,
%T 5949,7416,9145,11155,13486,16159,19218,22686,26611,31018,35959,41461,
%U 47580,54345,61816,70024,79033,88876,99621,111303,123994,137731,152590,168610,185871
%N Number of inequivalent ways of placing 2 nonattacking rooks on n X n board up to rotations and reflections of the board.
%H Leisure Maths Entertainment Forum, <a href="http://kuing.orzweb.net/viewthread.php?tid=6019">2 nonattacking rooks on n X n board</a>, Chinese blog.
%F a(n) = (1/16)*n*(n^3-2n^2+6n-4) if n is even;
%F a(n) = (1/16)*(n-1)*(n^3-n^2+5n-1) if n is odd.
%F G.f.: -x^2*(x^2+1)*(x^2+x+1)/((x+1)^2*(x-1)^5). - _Alois P. Heinz_, Apr 26 2019
%e For n = 4 the a(4) = 13 solutions are
%e {{1,0,0,0}} {{1,0,0,0}} {{1,0,0,0}}
%e {{0,1,0,0}} {{0,0,1,0}} {{0,0,0,1}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e —————————————————————————————————————
%e {{1,0,0,0}} {{1,0,0,0}} {{1,0,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e {{0,0,1,0}} {{0,0,0,1}} {{0,0,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,1}}
%e —————————————————————————————————————
%e {{0,1,0,0}} {{0,1,0,0}} {{0,1,0,0}}
%e {{1,0,0,0}} {{0,0,1,0}} {{0,0,0,1}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e —————————————————————————————————————
%e {{0,1,0,0}} {{0,1,0,0}} {{0,1,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,0,0}}
%e {{0,0,1,0}} {{0,0,0,1}} {{0,0,0,0}}
%e {{0,0,0,0}} {{0,0,0,0}} {{0,0,1,0}}
%e —————————————————————————————————————
%e {{0,0,0,0}}
%e {{0,1,0,0}}
%e {{0,0,1,0}}
%e {{0,0,0,0}}
%t Table[
%t Piecewise[{{(n (n^3 - 2 n^2 + 6 n - 4))/16, Mod[n, 2] == 0},
%t {((n - 1) (n^3 - n^2 + 5 n - 1))/16, Mod[n, 2] == 1}}],{n, 20}]
%Y Cf. A000903, A163102, A035287, A179058, A144084.
%K nonn,easy
%O 1,3
%A _Mo Li_, Apr 19 2019
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