OFFSET
0,1
COMMENTS
Alternatively, these are sets of subsets of {1..n} whose dual is a (strict) antichain, also called T_1 sets of subsets. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of sets, none of which is a subset of any other.
EXAMPLE
The a(0) = 2 through a(2) = 10 sets of subsets:
{} {} {}
{{}} {{}} {{}}
{{1}} {{1}}
{{},{1}} {{2}}
{{},{1}}
{{},{2}}
{{1},{2}}
{{},{1},{2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
MATHEMATICA
tmQ[eds_]:=Union@@Select[Intersection@@@Rest[Subsets[eds]], Length[#]==1&]==Union@@eds;
Table[Length[Select[Subsets[Subsets[Range[n]]], tmQ[#]&]], {n, 0, 3}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 10 2019
STATUS
approved