A306001 - OEIS

A306001

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

1, 1, 2, 8, 84, 13000

(list; graph; refs; listen; history; text; internal format)

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:

{}

{{1,3},{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