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A059050 Number of 7-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 7 labeled nodes with n (not necessary empty) distinct hyperedges (n=0,1,...,128). 4
0, 0, 0, 0, 0, 20580, 9106440, 1058272828, 56671435220, 1819138009252, 40526220292026, 685404291322800, 9333711208757096, 106588763704012184, 1051025434717631806, 9144977489478933912, 71381946761468630363 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..16.

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

Cf. A059048, A059049, A059051, A059052.

Sequence in context: A235831 A235587 A082254 * A056073 A173378 A028519

Adjacent sequences:  A059047 A059048 A059049 * A059051 A059052 A059053

KEYWORD

fini,nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

STATUS

approved

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Last modified January 26 13:42 EST 2022. Contains 350598 sequences. (Running on oeis4.)