A305999 Number of unlabeled spanning intersecting set-systems on n vertices with no singletons.

1, 0, 1, 6, 76, 12916

Offset

0,4

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. A singleton is an edge containing only one vertex.

Links

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

Formula

a(n) = A306001(n) - A306001(n-1) for n > 0. - Andrew Howroyd, Aug 12 2019

Example

Non-isomorphic representative of the a(3) = 6 set-systems:
{{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, A306000, A306001, A306008.

Sequence in context: A132613 A009763 A340886 * A274464 A028979 A082629

Adjacent sequences: A305996 A305997 A305998 * A306000 A306001 A306002

Keyword

nonn,more

Author

Gus Wiseman, Jun 16 2018

Extensions

a(5) from Andrew Howroyd, Aug 12 2019

Status

approved