A327808 Number of unlabeled, disconnected, nonempty antichains of subsets of {1..n}.

0, 0, 1, 3, 9, 32, 233, 16578

Offset

0,4

Comments

An antichain is a set of nonempty sets, none of which is a subset of any other. A singleton is considered to be connected.

Links

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

Formula

a(n) = A327424(n) - 1.

Example

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

Crossrefs

The labeled version is A327354 - 1.

The covering case is A327426.

Unlabeled antichains that are either not connected or not covering are A327437.

The version with empty antichains allowed is A327424.

Cf. A000372, A014466, A120338, A293606, A326704, A327062, A327355.

Sequence in context: A341302 A297209 A058138 * A284964 A344247 A333770

Adjacent sequences: A327805 A327806 A327807 * A327809 A327810 A327811

Keyword

nonn,more

Author

Gus Wiseman, Sep 26 2019

Status

approved