A327424 - OEIS

%I #6 Sep 26 2019 15:24:52

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

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

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

%e Non-isomorphic representatives of the a(0) = 1 through a(4) = 10 antichains:

%e   {}  {}  {}         {}             {}

%e           {{1},{2}}  {{1},{2}}      {{1},{2}}

%e                      {{1},{2,3}}    {{1},{2,3}}

%e                      {{1},{2},{3}}  {{1},{2},{3}}

%e                                     {{1},{2,3,4}}

%e                                     {{1,2},{3,4}}

%e                                     {{1},{2},{3,4}}

%e                                     {{1},{2},{3},{4}}

%e                                     {{1},{2,4},{3,4}}

%e                                     {{1},{2,3},{2,4},{3,4}}

%Y Partial sums of the positive-index terms of A327426.

%Y The covering case is A327426.

%Y The labeled version is A327354.

%Y The labeled covering case is A120338.

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

%Y The case without empty antichains is A327808.

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

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 26 2019