A321231 Number of non-isomorphic connected weight-n multiset partitions with no singletons and multiset density -1.

1, 0, 2, 3, 8, 15, 42, 94, 256, 656, 1807

Offset: 0

Author

Gus Wiseman, Oct 31 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) = 2 through a(5) = 15 multiset partitions:
  {{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}}
                      {{1,1},{1,1}}  {{1,2,3,4,4}}
                      {{1,2},{2,2}}  {{1,2,3,4,5}}
                      {{1,3},{2,3}}  {{1,1},{1,1,1}}
                                     {{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}}
                                     {{2,2},{1,2,2}}
                                     {{3,3},{1,2,3}}
		

Crossrefs

Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A317672, A318697, A321155, A321228, A321229.