A321680 Number of non-isomorphic weight-n connected antichains (not necessarily strict) of multisets with multiset density -1.

1, 1, 3, 4, 9, 14, 39, 80, 216, 538, 1460

Offset

0,3

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=0..10.

Example

Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset trees:
  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}        {{1,1,1,1,1}}
         {{1,2}}    {{1,2,2}}      {{1,1,2,2}}        {{1,1,2,2,2}}
         {{1},{1}}  {{1,2,3}}      {{1,2,2,2}}        {{1,2,2,2,2}}
                    {{1},{1},{1}}  {{1,2,3,3}}        {{1,2,2,3,3}}
                                   {{1,2,3,4}}        {{1,2,3,3,3}}
                                   {{1,1},{1,1}}      {{1,2,3,4,4}}
                                   {{1,2},{2,2}}      {{1,2,3,4,5}}
                                   {{1,3},{2,3}}      {{1,1},{1,2,2}}
                                   {{1},{1},{1},{1}}  {{1,2},{2,2,2}}
                                                      {{1,2},{2,3,3}}
                                                      {{1,3},{2,3,3}}
                                                      {{1,4},{2,3,4}}
                                                      {{3,3},{1,2,3}}
                                                      {{1},{1},{1},{1},{1}}

Crossrefs

Cf. A006126, A007718, A056156, A096827, A285572, A293993, A293994, A305052, A319719, A319721, A321194, A321585, A321681.

Sequence in context: A054162 A174783 A183203 * A215667 A125874 A216075

Adjacent sequences: A321677 A321678 A321679 * A321681 A321682 A321683

Keyword

nonn,more

Author

Gus Wiseman, Nov 16 2018

Status

approved