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Search: id:A059530
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| A059530 |
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Triangle T(n,k) of k-block T_0-tricoverings of an n-set. |
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+0
3
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| 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; listen)
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OFFSET
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3,6
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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. 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.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
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T_0-tricoverings of a 4-set
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FORMULA
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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!.
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EXAMPLE
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[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.
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CROSSREFS
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Cf. (column sums) A060069, (row sums) A060070, A060051-A060053, A002718, A059443, A003462, A059945-059951.
Sequence in context: A140334 A078529 A121383 this_sequence A049828 A058612 A099725
Adjacent sequences: A059527 A059528 A059529 this_sequence A059531 A059532 A059533
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 22 2001
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