login
A057223
Number of 4 X n binary matrices without unit columns up to row and column permutations.
8
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
0,2
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).
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).
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Sep 18 2000
EXTENSIONS
Added more terms, Joerg Arndt, May 21 2013
STATUS
approved