A319784 - OEIS

%I #6 Sep 28 2018 15:24:25

%S 1,1,0,1,1,1,3,5,7,14,25

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

%C A multiset partition is intersecting if no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict.

%e Non-isomorphic representatives of the a(1) = 1 through a(8) = 7 multiset partitions:

%e 1: {{1}}

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

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

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

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

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

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

%e 7: {{4},{1,3,4},{2,3,4}}

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

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

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

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

%e 8: {{1,5},{2,4,5},{3,4,5}}

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

%e    {{2,4},{1,2,5},{3,4,5}}

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

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

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

%e    {{1,5},{2,5},{3,5},{4,5}}

%Y Cf. A007716, A049311, A283877, A305843, A305854, A306006, A316980, A317752.

%Y Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319782, A319789.

%K nonn,more

%O 0,7

%A _Gus Wiseman_, Sep 27 2018