

A056164


Number of ordered antichain covers of an unlabeled nset; labeled T_1hypergraphs (without empty hyperedges) with n hyperedges.


0




OFFSET

1,2


COMMENTS

A T_1hypergraph 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, 127138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.


LINKS

Table of n, a(n) for n=1..5.
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers


FORMULA

a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of kelement ordered antichains covers of an unlabeled nset.


EXAMPLE

There are 6 ordered antichain covers on an unlabeled 3set: ({1,2,3}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).
a(3)=1+3+2=6; a(4)=1+6+17+25+30+30=109; a(5)=1+10+71+429+2176+8310+20580+38640+60480+60480=191177.


CROSSREFS

Cf. A056074, A056090, A056093, A000372, A056005, A056069A056071, A056073, A056046A056049, A056052, A056101, A056104, A051112A051118.
Sequence in context: A059088 A216151 A057771 * A156500 A264889 A231537
Adjacent sequences: A056161 A056162 A056163 * A056165 A056166 A056167


KEYWORD

hard,more,nonn


AUTHOR

Vladeta Jovovic, Goran Kilibarda, Jul 31 2000


STATUS

approved



