A305857 Number of unlabeled intersecting antichains on up to n vertices.

1, 2, 3, 6, 15, 87, 3528, 47174113

Offset

0,2

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.

Links

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

Formula

a(n) = A305855(0) + A305855(1) + ... + A305855(n). - Brendan McKay, May 11 2020

Example

Non-isomorphic representatives of the a(4) = 15 intersecting antichains:
  {}
  {{1}}
  {{1,2}}
  {{1,2,3}}
  {{1,2,3,4}}
  {{1,3},{2,3}}
  {{1,4},{2,3,4}}
  {{1,3,4},{2,3,4}}
  {{1,2},{1,3},{2,3}}
  {{1,4},{2,4},{3,4}}
  {{1,3},{1,4},{2,3,4}}
  {{1,2},{1,3,4},{2,3,4}}
  {{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, A305855, A305856.

Sequence in context: A116632 A214343 A007364 * A014627 A145781 A351880

Adjacent sequences: A305854 A305855 A305856 * A305858 A305859 A305860

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