A321253 - OEIS

%I #5 Nov 01 2018 18:22:34

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

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

%C 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.

%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(1) = 1 through a(5) = 28 multiset partitions:

%e   {{1}}  {{1,1}}  {{1,1,1}}    {{1,1,1,1}}      {{1,1,1,1,1}}

%e          {{1,2}}  {{1,2,2}}    {{1,1,2,2}}      {{1,1,2,2,2}}

%e                   {{1,2,3}}    {{1,2,2,2}}      {{1,2,2,2,2}}

%e                   {{1},{1,1}}  {{1,2,3,3}}      {{1,2,2,3,3}}

%e                   {{2},{1,2}}  {{1,2,3,4}}      {{1,2,3,3,3}}

%e                                {{1},{1,1,1}}    {{1,2,3,4,4}}

%e                                {{1},{1,2,2}}    {{1,2,3,4,5}}

%e                                {{1,2},{2,2}}    {{1},{1,1,1,1}}

%e                                {{1,3},{2,3}}    {{1,1},{1,1,1}}

%e                                {{2},{1,2,2}}    {{1,1},{1,2,2}}

%e                                {{3},{1,2,3}}    {{1},{1,2,2,2}}

%e                                {{1},{2},{1,2}}  {{1,2},{2,2,2}}

%e                                                 {{1,2},{2,3,3}}

%e                                                 {{1,3},{2,3,3}}

%e                                                 {{1,4},{2,3,4}}

%e                                                 {{2},{1,1,2,2}}

%e                                                 {{2},{1,2,2,2}}

%e                                                 {{2},{1,2,3,3}}

%e                                                 {{2,2},{1,2,2}}

%e                                                 {{3},{1,2,3,3}}

%e                                                 {{3,3},{1,2,3}}

%e                                                 {{4},{1,2,3,4}}

%e                                                 {{1},{1,2},{2,2}}

%e                                                 {{1},{2},{1,2,2}}

%e                                                 {{2},{1,2},{2,2}}

%e                                                 {{2},{1,3},{2,3}}

%e                                                 {{2},{3},{1,2,3}}

%e                                                 {{3},{1,3},{2,3}}

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

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Nov 01 2018