cp's OEIS Frontend

A322113 Number of non-isomorphic self-dual connected antichains of multisets of weight n.

%I A322113 #4 Nov 27 2018 16:18:20
%S A322113 1,1,1,1,2,2,3,5,10,18,30
%N A322113 Number of non-isomorphic self-dual connected antichains of multisets of weight n.
%C A322113 The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.
%C A322113 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 A322113 Non-isomorphic representatives of the a(1) = 1 through a(9) = 18 antichains:
%e A322113   {{1}}  {{11}}  {{111}}  {{1111}}    {{11111}}    {{111111}}
%e A322113                           {{12}{12}}  {{11}{122}}  {{112}{122}}
%e A322113                                                    {{12}{13}{23}}
%e A322113 .
%e A322113   {{1111111}}      {{11111111}}        {{111111111}}
%e A322113   {{111}{1222}}    {{111}{11222}}      {{1111}{12222}}
%e A322113   {{112}{1222}}    {{1112}{1222}}      {{1112}{11222}}
%e A322113   {{11}{12}{233}}  {{112}{12222}}      {{1112}{12222}}
%e A322113   {{12}{13}{233}}  {{1122}{1122}}      {{112}{122222}}
%e A322113                    {{11}{122}{233}}    {{11}{11}{12233}}
%e A322113                    {{12}{13}{2333}}    {{11}{122}{1233}}
%e A322113                    {{13}{112}{233}}    {{112}{123}{233}}
%e A322113                    {{13}{122}{233}}    {{113}{122}{233}}
%e A322113                    {{12}{13}{24}{34}}  {{12}{111}{2333}}
%e A322113                                        {{12}{13}{23333}}
%e A322113                                        {{12}{133}{2233}}
%e A322113                                        {{123}{123}{123}}
%e A322113                                        {{13}{112}{2333}}
%e A322113                                        {{22}{113}{2333}}
%e A322113                                        {{12}{13}{14}{234}}
%e A322113                                        {{12}{13}{22}{344}}
%e A322113                                        {{12}{13}{24}{344}}
%Y A322113 Cf. A006126, A007716, A007718, A286520, A293993, A293994, A304867, A316983, A318099, A319719, A319721, A322111, A322112.
%K A322113 nonn,more
%O A322113 0,5
%A A322113 _Gus Wiseman_, Nov 26 2018