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A056071 Number of 6-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 6 labeled nodes and n hyperedges. 3
30, 8340, 780242, 29813578, 657271645, 10037038800, 117733967666, 1130702091428, 9273992351046, 66900184307860, 433616524985590, 2566055594813118 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.

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=4..15.

K. S. Brown, Dedekind's problem

Eric Weisstein's World of Mathematics, Antichain covers

FORMULA

a(n)=C(n + 63, 63) - 30*C(n + 47, 47) + 120*C(n + 39, 39) + 60*C(n + 35, 35) + 60*C(n + 33, 33) - 12*C(n + 32, 32) - 345*C(n + 31, 31) - 720*C(n + 29, 29) + 810*C(n + 27, 27) + 120*C(n + 26, 26) + 480*C(n + 25, 25) + 360*C(n + 24, 24) - 480*C(n + 23, 23) - 720*C(n + 22, 22) - 240*C(n + 21, 21) - 540*C(n + 20, 20) + 1380*C(n + 19, 19) + 750*C(n + 18, 18) + 60*C(n + 17, 17) - 210*C(n + 16, 16) - 1535*C(n + 15, 15) - 1820*C(n + 14, 14) + 2250*C(n + 13, 13) + 1800*C(n + 12, 12) - 2820*C(n + 11, 11) + 300*C(n + 10, 10) + 2040*C(n + 9, 9) + 340*C(n + 8, 8) - 1815*C(n + 7, 7) + 510*C(n + 6, 6) - 1350*C(n + 5, 5) + 1350*C(n + 4, 4) + 274*C(n + 3, 3) - 548*C(n + 2, 2) + 120*C(n + 1, 1).

CROSSREFS

Cf. A051114 for 6-element (unordered) antichains on a labeled n-element set, A056005.

Sequence in context: A087216 A239925 A059049 * A299410 A294976 A294975

Adjacent sequences:  A056068 A056069 A056070 * A056072 A056073 A056074

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 26 2000

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)