|
| |
|
|
A060488
|
|
Number of 4-block ordered tricoverings of an unlabeled n-set.
|
|
3
| |
|
|
4, 13, 28, 50, 80, 119, 168, 228, 300, 385, 484, 598, 728, 875, 1040, 1224, 1428, 1653, 1900, 2170, 2464, 2783, 3128, 3500, 3900, 4329, 4788, 5278, 5800, 6355, 6944, 7568, 8228, 8925, 9660, 10434, 11248, 12103, 13000, 13940, 14924, 15953, 17028, 18150, 19320
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,1
|
|
|
COMMENTS
| A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
If Y is a 4-subset of an n-set X then, for n>=6, a(n-3) is the number of 3-subsets of X having at most one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 08 2007
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 3..1000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
|
|
|
FORMULA
| a(n)=binomial(n+3, 3)-6*binomial(n+1, 1)+8*binomial(n, 0)-3*binomial(n-1, -1).
G.f.: -y^3*(-4+3*y)/(-1+y)^4.
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! ).
a(n) = (n+9)*binomial(n-1, 2)/3.
a(n) = (n-2)*(n-1)*(n+9)/6. - Zak Seidov, Jun 15 2006
|
|
|
MATHEMATICA
| Table[ 3 (n - 1) (n - 2)/2! + n (n - 1) (n - 2)/3!, {n, 3, 62}] (* From Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
|
|
|
PROG
| (PARI) a(n)=(n-2)*(n-1)*(n+9)/6 \\ Charles R Greathouse IV, Jun 14 2011
(MAGMA) [(n-2)*(n-1)*(n+9)/6: n in [3..60]]; // Vincenzo Librandi, Jun 15 2011
|
|
|
CROSSREFS
| Essentially the same as A026054. - Vladeta Jovovic, Jun 15 2006
Cf. A006095, A060483-A060492, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.
Fourth column (m=3) of (1, 4)-Pascal triangle A095666.
Sequence in context: A155371 A155355 A155356 * A054968 A087035 A112560
Adjacent sequences: A060485 A060486 A060487 * A060489 A060490 A060491
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 20 2001
|
| |
|
|
