A306001 Number of unlabeled intersecting set-systems with no singletons on up to n vertices.

1, 1, 2, 8, 84, 13000

Offset

0,3

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. A singleton is an edge containing only one vertex.

Links

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

Formula

a(n) = A305856(n) - A000612(n). - Andrew Howroyd, Aug 12 2019

Example

Non-isomorphic representatives of the a(3) = 8 set-systems:
{}
{{1,2}}
{{1,2,3}}
{{1,3},{2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A051185, A048143, A261006, A058891, A261005, A304998, A305854-A305857, A305935, A305999, A306000.

Sequence in context: A261683 A134089 A136647 * A261730 A052456 A276991

Adjacent sequences: A305998 A305999 A306000 * A306002 A306003 A306004

Keyword

nonn,more

Author

Gus Wiseman, Jun 16 2018

Extensions

a(5) from Andrew Howroyd, Aug 12 2019

Status

approved