A326899 Number of unlabeled connectedness systems covering n vertices without singletons.

1, 0, 1, 4, 41, 3048, 26894637

Offset: 0

Author

Gus Wiseman, Aug 02 2019

Keywords

• nonn
• more

Comments

We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges.

Examples

			Non-isomorphic representatives of the a(3) = 4 connectedness systems:
  {{1,2,3}}
  {{2,3},{1,2,3}}
  {{1,3},{2,3},{1,2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}
		

Crossrefs

The case with singletons is A326871.

First differences of A072444 (the non-covering case).

Euler transform of A072445 (the connected case).

The labeled version is A326877.

Cf. A072446, A072447, A193674, A323818, A326866, A326867, A326868, A326869, A326870.

Extensions

a(6) corrected by Andrew Howroyd, Oct 28 2023