The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A059530 Triangle T(n,k) of k-block T_0-tricoverings of an n-set, n >= 3, k = 0..2*n. 7
 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 39, 89, 43, 3, 0, 0, 0, 0, 0, 252, 2192, 4090, 2435, 445, 12, 0, 0, 0, 0, 0, 1260, 37080, 179890, 289170, 188540, 50645, 4710, 70, 0, 0, 0, 0, 0, 5040, 536760, 6052730, 20660055, 29432319, 19826737, 6481160, 964495, 52430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,6 COMMENTS A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering. A covering of a set is a T_0-covering if for every two distinct elements of the set there exists a block of the covering containing one but not the other element. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. LINKS Andrew Howroyd, Table of n, a(n) for n = 3..1674 Vladeta Jovovic, T_0-tricoverings of a 4-set FORMULA E.g.f. for k-block T_0-tricoverings of an n-set is exp(-x+1/2*x^2+1/3*x^3*y)*Sum_{i=0..inf}(1+y)^binomial(i, 3)*exp(-1/2*x^2*(1+y)^i)*x^i/i!. T(n,k) = 0 for n > binomial(k, 3). - Andrew Howroyd, Jan 30 2020 EXAMPLE Triangle begins: [0, 0, 0, 0, 1, 3, 1], [0, 0, 0, 0, 1, 39, 89, 43, 3], [0, 0, 0, 0, 0, 252, 2192, 4090, 2435, 445, 12], [0, 0, 0, 0, 0, 1260, 37080, 179890, 289170, 188540, 50645, 4710, 70], ... There are 5 = 1 + 3 + 1 T_0-tricoverings of a 3-set and 175 = 1 + 39 + 89 + 43 + 3 T_0-tricoverings of a 4-set, cf. A060070. PROG (PARI) \\ gets k-th column as vector C(k)=if(k<4, [], Vecrev(serlaplace(polcoef(exp(-x + x^2/2 + x^3*y/3 + O(x*x^k))*sum(i=0, 2*k, (1+y)^binomial(i, 3)*exp(-x^2*(1+y)^i/2 + O(x*x^k))*x^i/i!), k))/y)) \\ Andrew Howroyd, Jan 30 2020 (PARI) T(n)={my(m=2*n, y='y + O('y^(n+1))); my(g=exp(-x + x^2/2 + x^3*y/3 + O(x*x^m))*sum(k=0, m, (1+y)^binomial(k, 3)*exp(-x^2*(1+y)^k/2 + O(x*x^m))*x^k/k!)); Mat([Col(serlaplace(p), -n) | p<-Vec(g)[2..m+1]]); } { my(A=T(8)); for(n=3, matsize(A)[1], print(concat([0], A[n, 1..2*n]))) } \\ Andrew Howroyd, Jan 30 2020 CROSSREFS Column sums are A060069. Row sums are A060070. Cf. A059443, A060052, A060092, A060487, A060492, A331039. Sequence in context: A078529 A180017 A243827 * A193525 A049828 A342557 Adjacent sequences: A059527 A059528 A059529 * A059531 A059532 A059533 KEYWORD nonn,tabf AUTHOR Vladeta Jovovic, Feb 22 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 03:10 EDT 2023. Contains 365781 sequences. (Running on oeis4.)