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

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

Offset

0,4

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.

Links

Table of n, a(n) for n=0..6.

Example

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.

Sequence in context: A059730 A006825 A333731 * A022500 A320335 A076652

Adjacent sequences: A326896 A326897 A326898 * A326900 A326901 A326902

Keyword

nonn,more

Author

Gus Wiseman, Aug 02 2019

Extensions

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

Status

approved