cp's OEIS Frontend

A319642 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of (not necessarily distinct) multisets.

%I A319642 #5 Sep 25 2018 20:48:09
%S A319642 1,1,2,3,6,9,16,25,42,66,108
%N A319642 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of (not necessarily distinct) multisets.
%C A319642 The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%C A319642 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e A319642 Non-isomorphic representatives of the a(1) = 1 through a(5) = 9 antichains:
%e A319642 1: {{1}}
%e A319642 2: {{1,1}}
%e A319642    {{1,2}}
%e A319642 3: {{1,1,1}}
%e A319642    {{1,2,2}}
%e A319642    {{1,2,3}}
%e A319642 4: {{1,1,1,1}}
%e A319642    {{1,1,2,2}}
%e A319642    {{1,2,2,2}}
%e A319642    {{1,2,3,3}}
%e A319642    {{1,2,3,4}}
%e A319642    {{1,2},{2,2}}
%e A319642 5: {{1,1,1,1,1}}
%e A319642    {{1,1,2,2,2}}
%e A319642    {{1,2,2,2,2}}
%e A319642    {{1,2,2,3,3}}
%e A319642    {{1,2,3,3,3}}
%e A319642    {{1,2,3,4,4}}
%e A319642    {{1,2,3,4,5}}
%e A319642    {{1,2},{2,2,2}}
%e A319642    {{3,3},{1,2,3}}
%Y A319642 Cf. A000219, A006126, A007716, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646.
%K A319642 nonn,more
%O A319642 0,3
%A A319642 _Gus Wiseman_, Sep 25 2018