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A321253
Number of non-isomorphic strict connected weight-n multiset partitions with multiset density -1.
5
0, 1, 2, 5, 12, 28, 78, 202, 578, 1650, 4904
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(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}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 01 2018
STATUS
approved