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

1,3

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.

Links

Table of n, a(n) for n=1..10.

Example

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.

Sequence in context: A075200 A075198 A294633 * A364267 A006405 A305189

Adjacent sequences: A320795 A320796 A320797 * A320799 A320800 A320801

Keyword

nonn,more

Author

Gus Wiseman, Nov 29 2018

Status

approved