A059083 Number of T_0-antichains on a labeled n-set.

2, 3, 3, 8, 96, 6373, 7725703, 2414518872815, 56130437161078967568912

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.

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..8.

V. Jovovic, 3-element T_0-antichains on a labeled 4-set

V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

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 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

Formula

a(n) = Sum_{m=0..binomial(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element T_0-antichains on a labeled n-set. Cf. A059080.

a(n) = column sums of A059080.

Example

a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 2 + 1, a(3) = 6 + 2, a(4) = 12 + 52 + 25 + 6 + 1, a(5) = 520 + 1770 + 2086 + 1370 + 490 + 115 + 20 + 2.

Crossrefs

Cf. A059079-A059082, A059048-A059052.

Cf. A000372.

Sequence in context: A263464 A267563 A166994 * A207626 A232324 A124931

Adjacent sequences: A059080 A059081 A059082 * A059084 A059085 A059086

Keyword

hard,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

Extensions

More terms from Vladeta Jovovic, Nov 28 2003

Status

approved