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A319566
Number of non-isomorphic connected T_0 set systems of weight n.
8
1, 1, 0, 1, 2, 3, 8, 17, 41, 103, 276
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.
EXAMPLE
Non-isomorphic 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}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 23 2018
STATUS
approved