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A320813 Number of non-isomorphic multiset partitions of weight n with no singletons in which all parts are aperiodic multisets. 13
1, 0, 1, 2, 5, 13, 33, 104, 293, 938, 2892 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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 row sums are all > 1 and (2) the positive entries in each row 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(2) = 1 through a(5) = 13 multiset partitions:

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

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

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

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

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

                                     {{1,2,3,4,5}}

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

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

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

                                     {{1,2},{3,4,5}}

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

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

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

CROSSREFS

Cf. A000740, A000837, A007716, A007916, A100953, A301700, A302545, A303386, A303546, A303707, A303708, A320797-A320813, A321283, A321390.

Sequence in context: A052988 A001429 A148288 * A278134 A271940 A273721

Adjacent sequences:  A320810 A320811 A320812 * A320814 A320815 A320816

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 08 2018

STATUS

approved

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)