OFFSET
4,1
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 = 4..200
Index entries for linear recurrences with constant coefficients, signature (110, -4991, 124120, -1887459, 18470550, -118758569, 501056740, -1355000500, 2223560000, -1973160000, 705600000).
FORMULA
a(n) = (1/7!)*(35^n - 7*20^n - 21*15^n + 42*10^n + 105*8^n + 105*7^n + 70*5^n - 945*4^n - 525*3^n + 2450*2^n - 1470).
E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..infinity}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).
G.f.: x^4*(27300000*x^7 +9288000*x^6 -17908650*x^5 +6008735*x^4 -796380*x^3 +38552*x^2 +210*x -43) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(7*x -1)*(8*x -1)*(10*x -1)*(15*x -1)*(20*x -1)*(35*x -1)). - Colin Barker, Jan 12 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Mar 20 2001
STATUS
approved