A305854 - OEIS

A305854

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

1, 1, 2, 10, 110, 14868

(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. S is spanning if every vertex is contained in some edge.

LINKS

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

FORMULA

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

EXAMPLE

Non-isomorphic representatives of the a(3) = 10 spanning intersecting set-systems:

{{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.

Sequence in context: A181445 A231969 A062499 * A234296 A049505 A136518

Adjacent sequences: A305851 A305852 A305853 * A305855 A305856 A305857

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 11 2018

EXTENSIONS

a(5) from Andrew Howroyd, Aug 12 2019

STATUS

approved