A057151 Number of square binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

1, 1, 2, 4, 8, 18, 41, 102, 252, 666, 1789, 5031, 14486, 43280, 132777, 420267, 1366307, 4566966, 15661086, 55081118, 198425478, 731661754, 2758808581, 10629386376, 41814350148, 167830018952, 686822393793, 2864024856054, 12162059027416, 52564545391789

Offset

1,3

Comments

Number of square binary matrices with n ones and with no zero rows or columns is A104602(n). - Vladeta Jovovic, Mar 25 2006

Also the number of non-isomorphic square set multipartitions (multisets of sets) of weight n. A multiset partition or hypergraph is square if its length (number of blocks or edges) is equal to its number of vertices. The weight of a multiset partition is the sum of sizes of its parts. - Gus Wiseman, Nov 16 2018

Links

Max Alekseyev, Table of n, a(n) for n = 1..30

Example

There are 666 square binary matrices with 10 ones, with no zero rows or columns, up to row and column permutation: 33 of size 4 X 4, 248 of size 5 X 5, 288 of size 6 X 6, 79 of size 7 X 7, 15 of size 8 X 8, 2 of size 9 X 9 and 1 of size 10 X 10. Cf. A057150.
From Gus Wiseman, Nov 16 2018: (Start)
Non-isomorphic representatives of the a(1) = 1 through a(6) = 18 square set multipartitions:
  {1}  {1}{2}  {2}{12}    {12}{12}      {1}{23}{23}      {12}{13}{23}
               {1}{2}{3}  {1}{1}{23}    {2}{13}{23}      {1}{23}{123}
                          {1}{3}{23}    {2}{3}{123}      {13}{23}{23}
                          {1}{2}{3}{4}  {3}{13}{23}      {3}{23}{123}
                                        {3}{3}{123}      {1}{1}{1}{234}
                                        {1}{2}{2}{34}    {1}{1}{24}{34}
                                        {1}{2}{4}{34}    {1}{1}{4}{234}
                                        {1}{2}{3}{4}{5}  {1}{2}{34}{34}
                                                         {1}{3}{24}{34}
                                                         {1}{3}{4}{234}
                                                         {1}{4}{24}{34}
                                                         {1}{4}{4}{234}
                                                         {2}{4}{12}{34}
                                                         {3}{4}{12}{34}
                                                         {4}{4}{12}{34}
                                                         {1}{2}{3}{3}{45}
                                                         {1}{2}{3}{5}{45}
                                                         {1}{2}{3}{4}{5}{6}
(End)

Crossrefs

Cf. A049311, A056037, A056079, A056080, A057149, A057150, A057152.

Cf. A054976, A101370, A104601, A104602, A120732, A283877, A319616.

Sequence in context: A112483 A151381 A306200 * A026699 A182780 A078678

Adjacent sequences: A057148 A057149 A057150 * A057152 A057153 A057154

Keyword

nonn

Author

Vladeta Jovovic, Aug 14 2000

Extensions

More terms from Max Alekseyev, May 31 2007

Status

approved