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.
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 31 2018
STATUS
approved