OFFSET
0,4
COMMENTS
A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
FORMULA
E.g.f. for ordered k-block tricoverings of an unlabeled n-set is exp(-x+x^2/2+x^3/3*y/(1-y))*Sum_{k=0..inf}1/(1-y)^binomial(k, 3)*exp(-x^2/2*1/(1-y)^n)*x^k/k!.
EXAMPLE
There are 184 ordered tricoverings of an unlabeled 3-set: 4 4-block, 60 5-block and 120 6-block tricoverings (cf. A060492).
PROG
(PARI) seq(n)={my(m=2*n\2, y='y + O('y^(n+1))); Vec(subst(Pol(serlaplace(exp(-x + x^2/2 + x^3*y/(3*(1-y)) + O(x*x^m))*sum(k=0, m, 1/(1-y)^binomial(k, 3)*exp((-x^2/2)/(1-y)^k + O(x*x^m))*x^k/k!))), x, 1))} \\ Andrew Howroyd, Jan 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Mar 20 2001
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 30 2020
STATUS
approved