A327355 Number of antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).

1, 1, 4, 14, 83, 1232, 84625, 109147467, 38634257989625

Offset: 0

Author

Gus Wiseman, Sep 10 2019

Keywords

• nonn
• more

Comments

An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.

The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.

Examples

			The a(1) = 1 through a(3) = 14 antichains:
  {}  {}         {}
      {{1}}      {{1}}
      {{2}}      {{2}}
      {{1},{2}}  {{3}}
                 {{1,2}}
                 {{1,3}}
                 {{2,3}}
                 {{1},{2}}
                 {{1},{3}}
                 {{2},{3}}
                 {{1},{2,3}}
                 {{2},{1,3}}
                 {{3},{1,2}}
                 {{1},{2},{3}}
		

Crossrefs

Column k = 0 of A327352.

The covering case is A120338.

The unlabeled version is A327437.

The non-spanning edge-connectivity version is A327354.

Cf. A014466, A327071, A327148, A327353, A327426.

Formula

a(n) = A120338(n) + A014466(n) - A006126(n).