A321739 Number of non-isomorphic weight-n set multipartitions (multisets of sets) whose part-sizes are also their vertex-degrees.

1, 1, 1, 2, 4, 6, 12, 21, 46, 94, 208

Offset

0,4

Comments

Also the number of (0,1) square matrices up to row and column permutations with n ones and no zero rows or columns, with the same multiset of row sums as of column sums.

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

Table of n, a(n) for n=0..10.

Example

Non-isomorphic representatives of the a(1) = 1 through a(6) = 12 set multipartitions:
  {1}  {1}{2}  {2}{12}    {12}{12}      {1}{23}{23}      {12}{13}{23}
               {1}{2}{3}  {1}{1}{23}    {2}{13}{23}      {3}{23}{123}
                          {1}{3}{23}    {3}{3}{123}      {1}{1}{1}{234}
                          {1}{2}{3}{4}  {1}{2}{2}{34}    {1}{1}{24}{34}
                                        {1}{2}{4}{34}    {1}{2}{34}{34}
                                        {1}{2}{3}{4}{5}  {1}{3}{24}{34}
                                                         {1}{4}{4}{234}
                                                         {2}{4}{12}{34}
                                                         {3}{4}{12}{34}
                                                         {1}{2}{3}{3}{45}
                                                         {1}{2}{3}{5}{45}
                                                         {1}{2}{3}{4}{5}{6}

Crossrefs

Cf. A000700, A049311, A057151, A104602, A319056, A320451, A321719, A321721, A321723, A321732, A321734, A321735, A321736, A321854.

Sequence in context: A105541 A105536 A328079 * A073660 A102588 A005303

Adjacent sequences: A321736 A321737 A321738 * A321740 A321741 A321742

Keyword

nonn,more

Author

Gus Wiseman, Nov 19 2018

Status

approved