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A320805
Number of non-isomorphic multiset partitions of weight n in which each part, as well as the multiset union of the parts, is an aperiodic multiset.
2
1, 1, 2, 6, 16, 55, 139, 516, 1500, 5269, 17017
OFFSET
0,3
COMMENTS
Also the number of nonnegative integer matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which (1) the positive entries in each row are relatively prime and (2) the column sums are relatively prime.
A multiset is aperiodic if its multiplicities are relatively prime.
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(4) = 16 multiset partitions:
{{1}} {{1,2}} {{1,2,2}} {{1,2,2,2}}
{{1},{2}} {{1,2,3}} {{1,2,3,3}}
{{1},{2,3}} {{1,2,3,4}}
{{2},{1,2}} {{1},{2,3,3}}
{{1},{2},{2}} {{1},{2,3,4}}
{{1},{2},{3}} {{1,2},{3,4}}
{{1,3},{2,3}}
{{2},{1,2,2}}
{{3},{1,2,3}}
{{1},{1},{2,3}}
{{1},{2},{3,4}}
{{1},{3},{2,3}}
{{2},{2},{1,2}}
{{1},{2},{2},{2}}
{{1},{2},{3},{3}}
{{1},{2},{3},{4}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 07 2018
STATUS
approved