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A059051 Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessary empty) distinct hyperedges. 2
2, 3, 2, 4, 99, 190866 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

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.

LINKS

Table of n, a(n) for n=0..5.

FORMULA

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.

EXAMPLE

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.

CROSSREFS

Cf. A059048-A059050, A059052.

Sequence in context: A236406 A202714 A022662 * A130069 A120007 A092509

Adjacent sequences:  A059048 A059049 A059050 * A059052 A059053 A059054

KEYWORD

hard,more,nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

STATUS

approved

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Last modified October 30 11:14 EDT 2014. Contains 248797 sequences.