A319764 - OEIS

%I #5 Sep 28 2018 15:22:29

%S 1,0,0,0,0,0,1,1,3,8,18

%N Number of non-isomorphic intersecting set systems of weight n with empty intersection.

%C A set system is a finite set of finite nonempty sets. It is intersecting if no two parts are disjoint. 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(6) = 1 through a(9) = 8 set systems:

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

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

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

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

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

%e 9: {{1,3},{1,4,5},{2,3,4,5}}

%e    {{1,5},{1,6},{2,3,4,5,6}}

%e    {{2,5},{1,2,6},{3,4,5,6}}

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

%e    {{1,3,5},{2,3,6},{4,5,6}}

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

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

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

%Y Cf. A007716, A281116, A283877, A305854, A306006, A316980, A317752, A317755, A317757, A318715, A318717.

%Y Cf. A319752, A319759, A319762, A319763, A319765, A319779, A319781.

%K nonn,more

%O 0,9

%A _Gus Wiseman_, Sep 27 2018