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A059051
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Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessary empty) distinct hyperedges.
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2
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OFFSET
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0,1
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COMMENTS
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An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.
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REFERENCES
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V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
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LINKS
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Table of n, a(n) for n=0..5.
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FORMULA
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a(n)=Sum_{m=0..C(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element ordered T_0-antichains on an unlabeled n-set. Cf. A059048.
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EXAMPLE
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a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 1 + 1, a(3) = 2 + 2, a(4) = 1 + 13 + 25 + 30 + 30, a(5) = 26 + 354 + 2086 + 8220 + 20580 + 38640 + 60480 + 60480. a(n) = column sums of A059048.
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CROSSREFS
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Cf. A059048-A059050, A059052.
Sequence in context: A127157 A202714 A022662 * A130069 A120007 A092509
Adjacent sequences: A059048 A059049 A059050 * A059052 A059053 A059054
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KEYWORD
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hard,more,nonn,changed
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AUTHOR
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Vladeta Jovovic, Goran Kilibarda, Dec 19 2000
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STATUS
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approved
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