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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..10.

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}}

CROSSREFS

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

Sequence in context: A147936 A147927 A147919 * A354083 A150029 A221841

Adjacent sequences:  A320802 A320803 A320804 * A320806 A320807 A320808

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 07 2018

STATUS

approved

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Last modified June 26 07:43 EDT 2022. Contains 354877 sequences. (Running on oeis4.)