A321253 Number of non-isomorphic strict connected weight-n multiset partitions with multiset density -1.

0, 1, 2, 5, 12, 28, 78, 202, 578, 1650, 4904

Offset: 0

Author

Gus Wiseman, Nov 01 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(1) = 1 through a(5) = 28 multiset partitions:
  {{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},{1,1}}  {{1,2,3,3}}      {{1,2,2,3,3}}
                  {{2},{1,2}}  {{1,2,3,4}}      {{1,2,3,3,3}}
                               {{1},{1,1,1}}    {{1,2,3,4,4}}
                               {{1},{1,2,2}}    {{1,2,3,4,5}}
                               {{1,2},{2,2}}    {{1},{1,1,1,1}}
                               {{1,3},{2,3}}    {{1,1},{1,1,1}}
                               {{2},{1,2,2}}    {{1,1},{1,2,2}}
                               {{3},{1,2,3}}    {{1},{1,2,2,2}}
                               {{1},{2},{1,2}}  {{1,2},{2,2,2}}
                                                {{1,2},{2,3,3}}
                                                {{1,3},{2,3,3}}
                                                {{1,4},{2,3,4}}
                                                {{2},{1,1,2,2}}
                                                {{2},{1,2,2,2}}
                                                {{2},{1,2,3,3}}
                                                {{2,2},{1,2,2}}
                                                {{3},{1,2,3,3}}
                                                {{3,3},{1,2,3}}
                                                {{4},{1,2,3,4}}
                                                {{1},{1,2},{2,2}}
                                                {{1},{2},{1,2,2}}
                                                {{2},{1,2},{2,2}}
                                                {{2},{1,3},{2,3}}
                                                {{2},{3},{1,2,3}}
                                                {{3},{1,3},{2,3}}
		

Crossrefs

Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A318697, A321155, A321194, A321228, A321229, A321254.