OFFSET
1,3
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 = 1..1000
FORMULA
a(n) = binomial(n+9, 9) - 15*binomial(n+3, 3) + 45*binomial(n+1, 1) - 40*binomial(n, 0) + 9*binomial(n-1, -1).
G.f.: y^3*(-225*y^3 + 60 - 225*y + 342*y^2 + 90*y^5 - 50*y^6 + 9*y^7)/(-1+y)^10.
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} 1/(1-y)^binomial(k, 3)*exp(-x^2/2*1/(1-y)^n)*x^k/k!.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Mar 20 2001
EXTENSIONS
a(1)=a(2)=0 prepended and terms a(30) and beyond from Andrew Howroyd, Jan 30 2020
STATUS
approved