A326904 Number of unlabeled set-systems (without {}) on n vertices that are closed under intersection.

1, 2, 4, 10, 38, 368, 29328, 216591692, 5592326399531792

Offset: 0

Author

Gus Wiseman, Aug 04 2019

Keywords

• nonn
• more

Comments

A set-system is a finite set of finite nonempty sets, so no two edges of such a set-system can be disjoint.

Apart from the offset the same as A193675. - R. J. Mathar, Aug 09 2019

Examples

			Non-isomorphic representatives of the a(0) = 1 through a(3) = 10 set-systems:
  {}  {}     {}           {}
      {{1}}  {{1}}        {{1}}
             {{1,2}}      {{1,2}}
             {{2},{1,2}}  {{1,2,3}}
                          {{2},{1,2}}
                          {{3},{1,2,3}}
                          {{2,3},{1,2,3}}
                          {{3},{1,3},{2,3}}
                          {{3},{2,3},{1,2,3}}
                          {{3},{1,3},{2,3},{1,2,3}}
		

Crossrefs

The covering case is A108800(n - 1).

The case with an edge containing all of the vertices is A193674(n - 1).

The case with union instead of intersection is A193674.

The labeled version is A326901.

Cf. A000798, A001930, A006058, A102895, A102898, A326876, A326866, A326878, A326882, A326903, A326906.

Formula

a(n > 0) = 2 * A193674(n - 1).