A321681 Number of non-isomorphic weight-n connected strict antichains of multisets with multiset density -1.

1, 1, 2, 3, 7, 13, 35, 77, 205, 517, 1399

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) = 13 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}}
                  {{1,2,3}}  {{1,2,2,2}}    {{1,2,2,2,2}}
                             {{1,2,3,3}}    {{1,2,2,3,3}}
                             {{1,2,3,4}}    {{1,2,3,3,3}}
                             {{1,2},{2,2}}  {{1,2,3,4,4}}
                             {{1,3},{2,3}}  {{1,2,3,4,5}}
                                            {{1,1},{1,2,2}}
                                            {{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}}

Crossrefs

Cf. A006126, A007718, A056156, A096827, A285572, A293993, A293994, A305052, A319557, A319565, A319719, A319721, A321585, A321680.

Sequence in context: A280765 A056953 A371867 * A045611 A006840 A123408

Adjacent sequences: A321678 A321679 A321680 * A321682 A321683 A321684

Keyword

nonn,more

Author

Gus Wiseman, Nov 16 2018

Status

approved