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 5-covers of an unlabeled n-set that cover 5 points of that set uniquely (if offset is 5).
LINKS
FORMULA
a(n)=(1/5!)*(Z(S_n; 27, 27, ...) + 10*Z(S_n; 13, 27, 13, 27, ...) + 15*Z(S_n; 7, 27, 7, 27, ...) + 20*Z(S_n; 6, 6, 27, 6, 6, 27, ...) + 20*Z(S_n; 4, 6, 13, 6, 4, 27, 4, 6, 13, 6, 4, 27, ...) + 30*Z(S_n; 3, 7, 3, 27, 3, 7, 3, 27, ...) + 24*Z(S_n; 2, 2, 2, 2, 27, 2, 2, 2, 2, 27, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n.
G.f. : 1/120*(1/(1 - x^1)^27 + 10/(1 - x^1)^13/(1 - x^2)^7 + 15/(1 - x^1)^7/(1 - x^2)^10 + 20/(1 - x^1)^6/(1 - x^3)^7 + 20/(1 - x^1)^4/(1 - x^2)^1/(1 - x^3)^3/(1 - x^6)^2 + 30/(1 - x^1)^3/(1 - x^2)^2/(1 - x^4)^5 + 24/(1 - x^1)^2/(1 - x^5)^5).
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 20 2000
STATUS
approved