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).
LINKS
V. Jovovic, Generating functions
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