A306007 - OEIS

%I #4 Jun 18 2018 08:58:37

%S 1,1,1,1,2,2,6,6,14,22

%N Number of non-isomorphic intersecting antichains of weight n.

%C An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. The weight of S is the sum of cardinalities of its elements. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(8) = 14 set-systems:

%e {{1,2,3,4,5,6,7,8}}

%e {{1,7},{2,3,4,5,6,7}}

%e {{1,2,7},{3,4,5,6,7}}

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

%e {{1,2,3,7},{4,5,6,7}}

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

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

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

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

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

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

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

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

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

%Y Cf. A007411, A007716, A034691, A048143, A049311, A116540, A283877, A293606, A293607, A304867, A305999, A305854-A305857, A306005-A306008.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Jun 16 2018