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Search: id:A060488
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| A060488 |
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Number of 4-block ordered tricoverings of an unlabeled n-set. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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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
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FORMULA
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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..inf}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
Essentially the same as A026054. - Vladeta Jovovic, Jun 15 2006
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CROSSREFS
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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.
Adjacent sequences: A060485 A060486 A060487 this_sequence A060489 A060490 A060491
Sequence in context: A024970 A079430 A056107 this_sequence A054968 A087035 A112560
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 20 2001
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