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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 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.)