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 A321412 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons and with aperiodic parts. 1
 1, 0, 0, 0, 1, 1, 3, 4, 12, 20, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS A multiset is aperiodic if its multiplicities are relatively prime. Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with no row or column having a common divisor > 1 or summing to 1. The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. 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(5) = 1 through a(8) = 12 multiset partitions: {{12}{12}}  {{12}{122}}  {{112}{122}}    {{112}{1222}}    {{1112}{1222}}                          {{12}{1222}}    {{12}{12222}}    {{112}{12222}}                          {{12}{13}{23}}  {{12}{13}{233}}  {{12}{122222}}                                          {{13}{23}{123}}  {{122}{11222}}                                                           {{12}{123}{233}}                                                           {{12}{13}{2333}}                                                           {{13}{112}{233}}                                                           {{13}{122}{233}}                                                           {{13}{23}{1233}}                                                           {{23}{123}{123}}                                                           {{12}{12}{34}{34}}                                                           {{12}{13}{24}{34}} CROSSREFS Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616. Cf. A320796, A320797, A320803, A320806, A320809, A320813, A321408, A321410, A321411. Sequence in context: A124817 A306005 A124818 * A124638 A124639 A279696 Adjacent sequences:  A321409 A321410 A321411 * A321413 A321414 A321415 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 16 2018 STATUS approved

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Last modified November 30 18:35 EST 2021. Contains 349424 sequences. (Running on oeis4.)