A326949 Number of unlabeled T_0 sets of subsets of {1..n}.

2, 4, 10, 68, 3838, 37320356

Offset: 0

Author

Gus Wiseman, Aug 08 2019

Keywords

• nonn
• more

Comments

The dual of a set-system 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}}. The T_0 condition means that the dual is strict (no repeated edges).

Examples

			Non-isomorphic representatives of the a(0) = 2 through a(2) = 10 sets of sets:
  {}    {}        {}
  {{}}  {{}}      {{}}
        {{1}}     {{1}}
        {{},{1}}  {{},{1}}
                  {{1},{2}}
                  {{2},{1,2}}
                  {{},{1},{2}}
                  {{},{2},{1,2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}
		

Crossrefs

The non-T_0 version is A003180.

The labeled version is A326941.

The covering case is A326942 (first differences).

The case without empty edges is A326946.

Cf. A000371, A000612, A003181, A059052, A245567, A316978, A319559, A319564, A319637, A326939, A326940.

Formula

a(n) = 2 * A326946(n).

Extensions

a(5) from Max Alekseyev, Oct 11 2023