cp's OEIS Frontend

A321405 Number of non-isomorphic self-dual set systems of weight n.

%I A321405 #5 Nov 15 2018 08:40:42
%S A321405 1,1,1,2,2,3,6,9,16,28,47
%N A321405 Number of non-isomorphic self-dual set systems of weight n.
%C A321405 Also the number of (0,1) symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows are all different.
%C A321405 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 A321405 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 A321405 Non-isomorphic representatives of the a(1) = 1 through a(8) = 16 set systems:
%e A321405   {{1}}  {{1}{2}}  {{2}{12}}    {{1}{3}{23}}    {{2}{13}{23}}
%e A321405                    {{1}{2}{3}}  {{1}{2}{3}{4}}  {{1}{2}{4}{34}}
%e A321405                                                 {{1}{2}{3}{4}{5}}
%e A321405 .
%e A321405   {{12}{13}{23}}        {{13}{23}{123}}          {{1}{13}{14}{234}}
%e A321405   {{3}{23}{123}}        {{1}{23}{24}{34}}        {{12}{13}{24}{34}}
%e A321405   {{1}{3}{24}{34}}      {{1}{4}{34}{234}}        {{1}{24}{34}{234}}
%e A321405   {{2}{4}{12}{34}}      {{2}{13}{24}{34}}        {{2}{14}{34}{234}}
%e A321405   {{1}{2}{3}{5}{45}}    {{3}{4}{14}{234}}        {{3}{4}{134}{234}}
%e A321405   {{1}{2}{3}{4}{5}{6}}  {{1}{2}{4}{35}{45}}      {{4}{13}{14}{234}}
%e A321405                         {{1}{3}{5}{23}{45}}      {{1}{2}{34}{35}{45}}
%e A321405                         {{1}{2}{3}{4}{6}{56}}    {{1}{2}{5}{45}{345}}
%e A321405                         {{1}{2}{3}{4}{5}{6}{7}}  {{1}{3}{24}{35}{45}}
%e A321405                                                  {{1}{4}{5}{25}{345}}
%e A321405                                                  {{2}{4}{12}{35}{45}}
%e A321405                                                  {{4}{5}{13}{23}{45}}
%e A321405                                                  {{1}{2}{3}{5}{46}{56}}
%e A321405                                                  {{1}{2}{4}{6}{34}{56}}
%e A321405                                                  {{1}{2}{3}{4}{5}{7}{67}}
%e A321405                                                  {{1}{2}{3}{4}{5}{6}{7}{8}}
%Y A321405 Cf. A000219, A007716, A045778, A049311, A135588, A138178, A283877, A316980, A316983, A319616.
%Y A321405 Cf. A320796, A320797, A321401, A321403, A321406.
%K A321405 nonn,more
%O A321405 0,4
%A A321405 _Gus Wiseman_, Nov 15 2018