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A319559
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Number of non-isomorphic T_0 set systems of weight n.
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42
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1, 1, 1, 2, 4, 7, 16, 35, 82, 200, 517
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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EXAMPLE
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Non-isomorphic 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}}
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CROSSREFS
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Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A305854, A306006, A316980, A317757.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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