

A319566


Number of nonisomorphic connected T_0 set systems of weight n.


7



1, 1, 0, 1, 2, 3, 8, 17, 41, 103, 276
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OFFSET

0,5


COMMENTS

In a set system, two vertices are equivalent if in every block the presence of the first is equivalent to the presence of the second. The T_0 condition means that there are no equivalent vertices.
The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.


LINKS

Table of n, a(n) for n=0..10.


EXAMPLE

Nonisomorphic representatives of the a(1) = 1 through a(6) = 8 set systems:
1: {{1}}
3: {{2},{1,2}}
4: {{1,3},{2,3}}
{{1},{2},{1,2}}
5: {{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
{{3},{1,3},{2,3}}
6: {{3},{1,4},{2,3,4}}
{{3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,3},{2,3}}


CROSSREFS

Cf. A007716, A007718, A049311, A056156, A059201, A283877, A316980.
Cf. A319557, A319558, A319559, A319560, A319564, A319565, A319567.
Sequence in context: A298405 A219788 A099965 * A294450 A345243 A292852
Adjacent sequences: A319563 A319564 A319565 * A319567 A319568 A319569


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 23 2018


STATUS

approved



