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Number of 6x6 binary matrices with n ones, with no zero rows or columns, up to row and column permutation.
4

%I #8 May 10 2013 12:44:30

%S 1,2,15,69,288,840,2144,4488,8317,13160,18636,23078,25856,25623,23187,

%T 18713,13932,9288,5816,3256,1767,858,419,180,88,34,16,6,3,1,1

%N Number of 6x6 binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

%C Sum_{k=0..36} a(n)=A054976(6).

%F G.f. : Z(S_6 X S_6; x_1, x_2, ...)-2*Z(S_6 X S_5; x_1, x_2, ...)+Z(S_5 X S_5; x_1, x_2, ...) if we replace x_i by 1+x^i, where Z(S_i X S_j; x_1, x_2, ...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j, respectively.

%Y Cf. A052370.

%K fini,full,nonn

%O 6,2

%A _Vladeta Jovovic_, Aug 04 2000