

A319559


Number of nonisomorphic T_0 set systems of weight n.


40



1, 1, 1, 2, 4, 7, 16, 35, 82, 200, 517
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OFFSET

0,4


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(5) = 7 set systems:
1: {{1}}
2: {{1},{2}}
3: {{2},{1,2}}
{{1},{2},{3}}
4: {{1,3},{2,3}}
{{1},{2},{1,2}}
{{1},{3},{2,3}}
{{1},{2},{3},{4}}
5: {{1},{2,4},{3,4}}
{{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
{{3},{1,3},{2,3}}
{{1},{2},{3},{2,3}}
{{1},{2},{4},{3,4}}
{{1},{2},{3},{4},{5}}


CROSSREFS

Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A305854, A306006, A316980, A317757.
Cf. A319557, A319558, A319560, A319564, A319565, A319566, A319567.
Sequence in context: A259544 A294376 A259545 * A260790 A151378 A192464
Adjacent sequences: A319556 A319557 A319558 * A319560 A319561 A319562


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 23 2018


STATUS

approved



