# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a060487 Showing 1-1 of 1 %I A060487 #10 Dec 23 2018 16:14:39 %S A060487 1,3,1,7,57,95,43,3,35,717,3107,4520,2465,445,12,155,7845,75835, %T A060487 244035,325890,195215,50825,4710,70,651,81333,1653771,10418070, %U A060487 27074575,33453959,20891962,6580070,965965,52430,465 %N A060487 Triangle T(n,k) of k-block tricoverings of an n-set (n >= 3, k >= 4). %C A060487 A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering. %H A060487 Andrew Howroyd, Table of n, a(n) for n = 3..1157 %F A060487 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..inf}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y). %e A060487 Triangle begins: %e A060487 [1, 3, 1]; %e A060487 [7, 57, 95, 43, 3]; %e A060487 [35, 717, 3107, 4520, 2465, 445, 12]; %e A060487 [155, 7845, 75835, 244035, 325890, 195215, 50825, 4710, 70]; %e A060487 [651, 81333, 1653771, 10418070, 27074575, 33453959, 20891962, 6580070, 965965, 52430, 465]; %e A060487 ... %e A060487 There are 205 tricoverings of a 4-set(cf. A060486): 7 4-block, 57 5-block, 95 6-block, 43 7-block and 3 8-block tricoverings. %o A060487 (PARI) %o A060487 WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} %o A060487 D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); WeighT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)} %o A060487 row(n, k)={my(m=n*k+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))/(y+x))); if(n==0, 1, (-1)^m*sum(j=0, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*q[#q-j])*y^(m-n)/(1+y))} %o A060487 for(n=3, 8, print(Vecrev(row(3,n)))); \\ _Andrew Howroyd_, Dec 23 2018 %Y A060487 Columns include A060483, A060484, A060485. %Y A060487 Row sums are A060486. %Y A060487 Cf. A006095, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951. %K A060487 nonn,tabf %O A060487 3,2 %A A060487 _Vladeta Jovovic_, Mar 20 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE