A059051 Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessarily empty) distinct hyperedges.

2, 3, 2, 4, 99, 190866

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, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

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

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

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.

a(n) = column sums of 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.

Crossrefs

Cf. A059048-A059050, A059052.

Sequence in context: A202714 A022662 A295703 * 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