cp's OEIS Frontend

A321411 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime.

%I A321411 #4 Nov 16 2018 07:49:15
%S A321411 1,0,0,0,0,1,0,4,6,16,25
%N A321411 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime.
%C A321411 A multiset is aperiodic if its multiplicities are relatively prime.
%C A321411 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 relatively prime row sums (or column sums) and no row or column having a common divisor > 1 or summing to 1.
%C A321411 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 A321411 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 A321411 Non-isomorphic representatives of the a(5) = 1 through a(9) = 16 multiset partitions:
%e A321411   {{12}{122}}  {{112}{1222}}    {{112}{12222}}    {{1112}{11222}}
%e A321411                {{12}{12222}}    {{122}{11222}}    {{1112}{12222}}
%e A321411                {{12}{13}{233}}  {{12}{123}{233}}  {{12}{1222222}}
%e A321411                {{13}{23}{123}}  {{13}{112}{233}}  {{12}{123}{2333}}
%e A321411                                 {{13}{122}{233}}  {{12}{13}{23333}}
%e A321411                                 {{23}{123}{123}}  {{12}{223}{1233}}
%e A321411                                                   {{13}{112}{2333}}
%e A321411                                                   {{13}{223}{1233}}
%e A321411                                                   {{13}{23}{12333}}
%e A321411                                                   {{23}{122}{1233}}
%e A321411                                                   {{23}{123}{1233}}
%e A321411                                                   {{12}{12}{34}{234}}
%e A321411                                                   {{12}{12}{34}{344}}
%e A321411                                                   {{12}{13}{14}{234}}
%e A321411                                                   {{12}{13}{24}{344}}
%e A321411                                                   {{12}{14}{34}{234}}
%Y A321411 Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616.
%Y A321411 Cf. A320796, A320797, A320803, A320806, A320809, A320813, A321283, A321408-A321413.
%K A321411 nonn,more
%O A321411 0,8
%A A321411 _Gus Wiseman_, Nov 16 2018