A322138 - OEIS

%I #4 Nov 28 2018 08:03:18

%S 1,0,2,3,7,7,20,26,78,184,553

%N Number of non-isomorphic weight-n blobs (2-connected weak antichains) of multisets with no singletons.

%C 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 Non-isomorphic representatives of the a(2) = 2 through a(7) = 26 blobs:

%e   {{11}}  {{111}}  {{1111}}    {{11111}}  {{111111}}      {{1111111}}

%e   {{12}}  {{122}}  {{1122}}    {{11222}}  {{111222}}      {{1112222}}

%e           {{123}}  {{1222}}    {{12222}}  {{112222}}      {{1122222}}

%e                    {{1233}}    {{12233}}  {{112233}}      {{1122333}}

%e                    {{1234}}    {{12333}}  {{122222}}      {{1222222}}

%e                    {{11}{11}}  {{12344}}  {{122333}}      {{1222333}}

%e                    {{12}{12}}  {{12345}}  {{123333}}      {{1223333}}

%e                                           {{123344}}      {{1223344}}

%e                                           {{123444}}      {{1233333}}

%e                                           {{123455}}      {{1233444}}

%e                                           {{123456}}      {{1234444}}

%e                                           {{111}{111}}    {{1234455}}

%e                                           {{112}{122}}    {{1234555}}

%e                                           {{122}{122}}    {{1234566}}

%e                                           {{123}{123}}    {{1234567}}

%e                                           {{123}{233}}    {{112}{1222}}

%e                                           {{134}{234}}    {{122}{1233}}

%e                                           {{11}{11}{11}}  {{123}{2233}}

%e                                           {{12}{12}{12}}  {{123}{2333}}

%e                                           {{12}{13}{23}}  {{123}{2344}}

%e                                                           {{134}{2344}}

%e                                                           {{145}{2345}}

%e                                                           {{223}{1233}}

%e                                                           {{344}{1234}}

%e                                                           {{12}{13}{233}}

%e                                                           {{13}{14}{234}}

%Y Cf. A002218, A007718, A013922, A275307, A286520, A293994, A304118, A304887, A319719, A322110, A322117, A322118.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Nov 27 2018