A327424 Number of unlabeled, non-connected or empty antichains of nonempty subsets of {1..n}.

1, 1, 2, 4, 10, 33, 234, 16579

Offset

0,3

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.

Example

Non-isomorphic representatives of the a(0) = 1 through a(4) = 10 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}}
                                    {{1},{2,4},{3,4}}
                                    {{1},{2,3},{2,4},{3,4}}

Crossrefs

Partial sums of the positive-index terms of A327426.

The covering case is A327426.

The labeled version is A327354.

The labeled covering case is A120338.

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

The case without empty antichains is A327808.

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

Sequence in context: A173489 A089476 A323207 * A220028 A006397 A297197

Adjacent sequences: A327421 A327422 A327423 * A327425 A327426 A327427

Keyword

nonn,more

Author

Gus Wiseman, Sep 26 2019

Status

approved