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%I #14 May 21 2013 10:03:08
%S 1,4,14,44,127,335,830,1931,4258,8943,17984,34765,64873,117220,205718,
%T 351552,586348,956393,1528350,2396631,3693123,5599550,8363304,
%U 12317274,17904795,25710327,36497466,51255153,71253960,98113791,133885404,181147299,243121170,323807952,428148174
%N Number of 4 X n binary matrices without unit columns up to row and column permutations.
%C A unit column of a binary matrix is a column with only one 1. First differences of a(n) give number of minimal 4-covers of an unlabeled n-set that cover 4 points of that set uniquely (if offset is 4).
%H V. Jovovic, <a href="/A057222/a057222.pdf">Generating functions</a>
%F 1/24*(Z(S_n; 12, 12, ...) + 8*Z(S_n; 3, 3, 12, 3, 3, 12, ...) + 6*Z(S_n; 6, 12, 6, 12, ...) + 3*Z(S_n; 4, 12, 4, 12, ...) + 6*Z(S_n; 2, 4, 2, 12, 2, 4, 2, 12, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n.
%F G.f. : 1/24*(1/(1 - x)^12 + 8/(1 - x)^3/(1 - x^3)^3 + 6/(1 - x)^6/(1 - x^2)^3 + 3/(1 - x)^4/(1 - x^2)^4 + 6/(1 - x)^2/(1 - x^2)/(1 - x^4)^2).
%o (PARI) x='x+O('x^66); Vec(1/24*(1/(1-x)^12 + 8/(1-x)^3/(1-x^3)^3 + 6/(1-x)^6/(1-x^2)^3 + 3/(1-x)^4/(1-x^2)^4 + 6/(1-x)^2/(1-x^2)/(1-x^4)^2)) \\ _Joerg Arndt_, May 21 2013
%Y Cf. A057524, A001752, A056885, A057222.
%K nonn
%O 0,2
%A _Vladeta Jovovic_, Sep 18 2000
%E Added more terms, _Joerg Arndt_, May 21 2013
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