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A319566 Number of non-isomorphic connected T_0 set systems of weight n. 7

%I

%S 1,1,0,1,2,3,8,17,41,103,276

%N Number of non-isomorphic connected T_0 set systems of weight n.

%C 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.

%C The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(1) = 1 through a(6) = 8 set systems:

%e 1: {{1}}

%e 3: {{2},{1,2}}

%e 4: {{1,3},{2,3}}

%e {{1},{2},{1,2}}

%e 5: {{2},{3},{1,2,3}}

%e {{2},{1,3},{2,3}}

%e {{3},{1,3},{2,3}}

%e 6: {{3},{1,4},{2,3,4}}

%e {{3},{2,3},{1,2,3}}

%e {{1,2},{1,3},{2,3}}

%e {{1,3},{2,4},{3,4}}

%e {{1,4},{2,4},{3,4}}

%e {{1},{2},{3},{1,2,3}}

%e {{1},{2},{1,3},{2,3}}

%e {{2},{3},{1,3},{2,3}}

%Y Cf. A007716, A007718, A049311, A056156, A059201, A283877, A316980.

%Y Cf. A319557, A319558, A319559, A319560, A319564, A319565, A319567.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Sep 23 2018

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Last modified July 28 09:54 EDT 2021. Contains 346326 sequences. (Running on oeis4.)