Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Nov 15 2018 08:40:50
%S 1,0,0,0,0,0,1,1,1,2,4
%N Number of non-isomorphic self-dual set systems of weight n with no singletons.
%C Also the number of 0-1 symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows are all different and none sums to 1.
%C 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}}.
%C The weight of a multiset partition 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(6) = 1 through a(10) = 4 set systems:
%e 6: {{1,2},{1,3},{2,3}}
%e 7: {{1,3},{2,3},{1,2,3}}
%e 8: {{1,2},{1,3},{2,4},{3,4}}
%e 9: {{1,2},{1,3},{1,4},{2,3,4}}
%e 9: {{1,2},{1,4},{3,4},{2,3,4}}
%e 10: {{1,2},{2,4},{1,3,4},{2,3,4}}
%e 10: {{1,3},{2,4},{1,3,4},{2,3,4}}
%e 10: {{1,4},{2,4},{3,4},{1,2,3,4}}
%e 10: {{1,2},{1,3},{2,4},{3,5},{4,5}}
%Y Cf. A000219, A007716, A045778, A049311, A135588, A138178, A283877, A302545, A316980, A316983.
%Y Cf. A320796, A320797, A321401, A321402, A321403, A321405.
%K nonn,more
%O 0,10
%A _Gus Wiseman_, Nov 15 2018