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

2, 4, 10, 68, 3838, 37320356

Offset

0,1

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).

Links

Table of n, a(n) for n=0..5.

Formula

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

Example

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.

Sequence in context: A326325 A080090 A125263 * A215439 A120402 A182238

Adjacent sequences: A326946 A326947 A326948 * A326950 A326951 A326952

Keyword

nonn,more

Author

Gus Wiseman, Aug 08 2019

Extensions

a(5) from Max Alekseyev, Oct 11 2023

Status

approved