A060489 Number of 5-block ordered tricoverings of an unlabeled n-set.

0, 0, 60, 375, 1392, 4020, 9960, 22200, 45730, 88543, 163000, 287650, 489610, 807625, 1295944, 2029165, 3108220, 4667690, 6884660, 9989345, 14277740, 20126570, 28010840, 38524310, 52403246, 70553825, 94083600, 124337460, 162938550, 211834647, 273350520, 350246835

Offset: 1

Author

Vladeta Jovovic, Mar 20 2001

Keywords

• nonn

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

Crossrefs

Column k=5 of A060492.

Cf. A060093, A060483, A060491.

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!.

Extensions

a(1)=a(2)=0 prepended and terms a(30) and beyond from Andrew Howroyd, Jan 30 2020