A322138 Number of non-isomorphic weight-n blobs (2-connected weak antichains) of multisets with no singletons.

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

Offset

0,3

Comments

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

Table of n, a(n) for n=0..10.

Example

Non-isomorphic representatives of the a(2) = 2 through a(7) = 26 blobs:
  {{11}}  {{111}}  {{1111}}    {{11111}}  {{111111}}      {{1111111}}
  {{12}}  {{122}}  {{1122}}    {{11222}}  {{111222}}      {{1112222}}
          {{123}}  {{1222}}    {{12222}}  {{112222}}      {{1122222}}
                   {{1233}}    {{12233}}  {{112233}}      {{1122333}}
                   {{1234}}    {{12333}}  {{122222}}      {{1222222}}
                   {{11}{11}}  {{12344}}  {{122333}}      {{1222333}}
                   {{12}{12}}  {{12345}}  {{123333}}      {{1223333}}
                                          {{123344}}      {{1223344}}
                                          {{123444}}      {{1233333}}
                                          {{123455}}      {{1233444}}
                                          {{123456}}      {{1234444}}
                                          {{111}{111}}    {{1234455}}
                                          {{112}{122}}    {{1234555}}
                                          {{122}{122}}    {{1234566}}
                                          {{123}{123}}    {{1234567}}
                                          {{123}{233}}    {{112}{1222}}
                                          {{134}{234}}    {{122}{1233}}
                                          {{11}{11}{11}}  {{123}{2233}}
                                          {{12}{12}{12}}  {{123}{2333}}
                                          {{12}{13}{23}}  {{123}{2344}}
                                                          {{134}{2344}}
                                                          {{145}{2345}}
                                                          {{223}{1233}}
                                                          {{344}{1234}}
                                                          {{12}{13}{233}}
                                                          {{13}{14}{234}}

Crossrefs

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

Sequence in context: A309666 A085420 A027672 * A104138 A281909 A083809

Adjacent sequences: A322135 A322136 A322137 * A322139 A322140 A322141

Keyword

nonn,more

Author

Gus Wiseman, Nov 27 2018

Status

approved