A305855 Number of unlabeled spanning intersecting antichains on n vertices.

1, 1, 1, 3, 9, 72, 3441, 47170585

Offset

0,4

Comments

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.

Links

Table of n, a(n) for n=0..7.

Formula

a(n) = A305857(n) - A305857(n-1) for n > 0. - Andrew Howroyd, Aug 13 2019

Example

Non-isomorphic representatives of the a(4) = 9 spanning intersecting antichains:
  {{1,2,3,4}}
  {{1,4},{2,3,4}}
  {{1,3,4},{2,3,4}}
  {{1,2},{1,3,4},{2,3,4}}
  {{1,3},{1,4},{2,3,4}}
  {{1,4},{2,4},{3,4}}
  {{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{1,4},{2,3,4}}
  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

Crossrefs

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305854-A305857.

Sequence in context: A163632 A321541 A102322 * A018576 A027290 A131496

Adjacent sequences: A305852 A305853 A305854 * A305856 A305857 A305858

Keyword

nonn,more

Author

Gus Wiseman, Jun 11 2018

Extensions

a(6) from Andrew Howroyd, Aug 13 2019

a(7) from Brendan McKay, May 11 2020

Status

approved