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A321283 Number of non-isomorphic multiset partitions of weight n in which the part sizes are relatively prime. 9
1, 1, 2, 7, 21, 84, 214, 895, 2607, 9591, 31134 (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 the row sums are relatively prime.

Also the number of non-isomorphic multiset partitions of weight n in which the multiset union of the parts is aperiodic, where 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) = 21 multiset partitions with relatively prime part-sizes:

  {{1}}  {{1},{1}}  {{1},{1,1}}    {{1},{1,1,1}}

         {{1},{2}}  {{1},{2,2}}    {{1},{1,2,2}}

                    {{1},{2,3}}    {{1},{2,2,2}}

                    {{2},{1,2}}    {{1},{2,3,3}}

                    {{1},{1},{1}}  {{1},{2,3,4}}

                    {{1},{2},{2}}  {{2},{1,2,2}}

                    {{1},{2},{3}}  {{3},{1,2,3}}

                                   {{1},{1},{1,1}}

                                   {{1},{1},{2,2}}

                                   {{1},{1},{2,3}}

                                   {{1},{2},{1,2}}

                                   {{1},{2},{2,2}}

                                   {{1},{2},{3,3}}

                                   {{1},{2},{3,4}}

                                   {{1},{3},{2,3}}

                                   {{2},{2},{1,2}}

                                   {{1},{1},{1},{1}}

                                   {{1},{1},{2},{2}}

                                   {{1},{2},{2},{2}}

                                   {{1},{2},{3},{3}}

                                   {{1},{2},{3},{4}}

Non-isomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions with aperiodic multiset union:

  {{1}}  {{1,2}}    {{1,2,2}}      {{1,2,2,2}}

         {{1},{2}}  {{1,2,3}}      {{1,2,3,3}}

                    {{1},{2,2}}    {{1,2,3,4}}

                    {{1},{2,3}}    {{1},{2,2,2}}

                    {{2},{1,2}}    {{1,2},{2,2}}

                    {{1},{2},{2}}  {{1},{2,3,3}}

                    {{1},{2},{3}}  {{1,2},{3,3}}

                                   {{1},{2,3,4}}

                                   {{1,2},{3,4}}

                                   {{1,3},{2,3}}

                                   {{2},{1,2,2}}

                                   {{3},{1,2,3}}

                                   {{1},{1},{2,3}}

                                   {{1},{2},{2,2}}

                                   {{1},{2},{3,3}}

                                   {{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, A303431, A303546, A303547, A320800-A320810.

Sequence in context: A150305 A150306 A150307 * A150308 A150309 A150310

Adjacent sequences:  A321280 A321281 A321282 * A321284 A321285 A321286

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 06 2018

STATUS

approved

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Last modified September 18 14:45 EDT 2020. Contains 337169 sequences. (Running on oeis4.)