A305854 Number of unlabeled spanning intersecting set-systems on n vertices.

1, 1, 2, 10, 110, 14868, 1289830592

Offset: 0

Author

Gus Wiseman, Jun 11 2018

Keywords

• nonn
• more

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.

Examples

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

Crossrefs

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305855-A305857.

Formula

a(n) = A305856(n) - A305856(n-1) for n > 0. - Andrew Howroyd, Aug 12 2019

Extensions

a(5) from Andrew Howroyd, Aug 12 2019

a(6) from Bert Dobbelaere, Apr 28 2025