A057223 Number of 4 X n binary matrices without unit columns up to row and column permutations.

1, 4, 14, 44, 127, 335, 830, 1931, 4258, 8943, 17984, 34765, 64873, 117220, 205718, 351552, 586348, 956393, 1528350, 2396631, 3693123, 5599550, 8363304, 12317274, 17904795, 25710327, 36497466, 51255153, 71253960, 98113791, 133885404, 181147299, 243121170, 323807952, 428148174

Offset: 0

Author

Vladeta Jovovic, Sep 18 2000

Keywords

• nonn

Comments

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).

Links

• V. Jovovic, Generating functions

Crossrefs

Cf. A057524, A001752, A056885, A057222.

Programs

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

Formula

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.

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).

Extensions

Added more terms, Joerg Arndt, May 21 2013