cp's OEIS Frontend

A321408 Number of non-isomorphic self-dual multiset partitions of weight n whose parts are aperiodic.

%I A321408 #4 Nov 16 2018 07:48:51
%S A321408 1,1,1,2,5,9,18,35,75,153,318
%N A321408 Number of non-isomorphic self-dual multiset partitions of weight n whose parts are aperiodic.
%C A321408 A multiset is aperiodic if its multiplicities are relatively prime.
%C A321408 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, in which no row or column has a common divisor > 1.
%C A321408 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}}.
%C A321408 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e A321408 Non-isomorphic representatives of the a(1) = 1 through a(6) = 18 multiset partitions:
%e A321408   {1}  {1}{2}  {2}{12}    {12}{12}      {12}{122}        {112}{122}
%e A321408                {1}{2}{3}  {2}{122}      {2}{1222}        {12}{1222}
%e A321408                           {1}{1}{23}    {1}{23}{23}      {2}{12222}
%e A321408                           {1}{3}{23}    {1}{3}{233}      {12}{13}{23}
%e A321408                           {1}{2}{3}{4}  {2}{13}{23}      {1}{23}{233}
%e A321408                                         {3}{3}{123}      {1}{3}{2333}
%e A321408                                         {1}{2}{2}{34}    {2}{13}{233}
%e A321408                                         {1}{2}{4}{34}    {3}{23}{123}
%e A321408                                         {1}{2}{3}{4}{5}  {3}{3}{1233}
%e A321408                                                          {1}{1}{1}{234}
%e A321408                                                          {1}{2}{34}{34}
%e A321408                                                          {1}{2}{4}{344}
%e A321408                                                          {1}{3}{24}{34}
%e A321408                                                          {1}{4}{4}{234}
%e A321408                                                          {2}{4}{12}{34}
%e A321408                                                          {1}{2}{3}{3}{45}
%e A321408                                                          {1}{2}{3}{5}{45}
%e A321408                                                          {1}{2}{3}{4}{5}{6}
%Y A321408 Cf. A000219, A007716, A120733, A138178, A316983, A319616.
%Y A321408 Cf. A320796, A320797, A320803, A320804, A320805, A320806, A320807, A320809, A320813, A321410, A321411, A321412.
%K A321408 nonn,more
%O A321408 0,4
%A A321408 _Gus Wiseman_, Nov 16 2018