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.

1, 1, 2, 6, 16, 55, 139, 516, 1500, 5269, 17017

Offset: 0

Author

Gus Wiseman, Nov 07 2018

Keywords

• nonn
• more

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.

Examples

			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}}
		

Crossrefs

Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303546, A303707, A303708, A303710, A320800-A320810, A321283.