OFFSET
0,6
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
Sean A. Irvine, Table of n, a(n) for n = 0..128
FORMULA
a(n)=C(128, n) - 42*C(96, n) + 210*C(80, n) + 140*C(72, n) + 210*C(68, n) - 84*C(66, n) + 14 *C(65, n) - 819*C(64, n) - 2520*C(60, n) + 2730*C(56, n) + 840*C(54, n) + 840*C(52, n) - 420*C(51, n) + 2940*C(50, n) + 630*C(48, n) - 5040*C(46, n) + 840*C(45, n) - 1260*C(44, n) + 1680*C(43, n) - 9660*C(42, n) + 1260*C(41, n) + 3360*C(40, n) - 7560*C(39, n) + 11130*C(38, n) + 5880*C(37, n) + 9240*C(36, n) + 2982*C(35, n) - 6300*C(34, n) - 8652 *C(33, n) - 9905*C(32, n) - 8400*C(31, n) - 8540*C(30, n) + 13860*C(29, n) + 14490 *C( 28, n) - 5040*C(27, n) + 10500*C(26, n) + 10080*C(25, n) - 8120*C(24, n) - 15050*C(23, n) - 5040*C(22, n) - 11340*C(21, n) + 20580*C(20, n) + 15750*C(19, n) - 1540*C(18, n) - 5810*C(17, n) - 16485*C(16, n) - 21420*C(15, n) + 26250*C(14, n) + 21000*C(13, n) - 29820*C(12, n) + 3500*C(11, n) + 17640*C(10, n) + 2940*C(9, n) - 16016*C(8, n) + 4410*C(7, n) - 9744*C(6, n) + 9744*C(5, n) + 1764*C(4, n) - 3528*C(3, n) + 720*C(2, n).
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Dec 19 2000
STATUS
approved