A320798 Number of non-isomorphic weight-n connected antichains of non-constant multisets with multiset density -1.

0, 1, 2, 5, 9, 24, 51, 134, 328, 868

Offset: 1

Author

Gus Wiseman, Nov 29 2018

Keywords

• nonn
• more

Comments

The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.

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

Examples

			Non-isomorphic representatives of the a(2) = 1 through a(6) = 24 multiset partitions:
  {{12}}  {{122}}  {{1122}}    {{11222}}    {{111222}}
          {{123}}  {{1222}}    {{12222}}    {{112222}}
                   {{1233}}    {{12233}}    {{112233}}
                   {{1234}}    {{12333}}    {{122222}}
                   {{13}{23}}  {{12344}}    {{122333}}
                               {{12345}}    {{123333}}
                               {{12}{233}}  {{123344}}
                               {{13}{233}}  {{123444}}
                               {{14}{234}}  {{123455}}
                                            {{123456}}
                                            {{112}{233}}
                                            {{122}{233}}
                                            {{12}{2333}}
                                            {{123}{344}}
                                            {{124}{344}}
                                            {{125}{345}}
                                            {{13}{2233}}
                                            {{13}{2333}}
                                            {{13}{2344}}
                                            {{133}{233}}
                                            {{14}{2344}}
                                            {{15}{2345}}
                                            {{13}{24}{34}}
                                            {{14}{24}{34}}
		

Crossrefs

Cf. A007716, A007718, A286520, A304867, A319719, A319721, A321155, A321760, A322111, A322113.