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

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

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

Keywords

• hard
• nonn

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.

Examples

			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.
		

References

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

Links

• 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).

Crossrefs

Cf. A059079-A059082, A059048-A059052.

Cf. A000372.

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.

Extensions

More terms from Vladeta Jovovic, Nov 28 2003