cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A057151 #13 Nov 18 2018 20:43:11
%S A057151 1,1,2,4,8,18,41,102,252,666,1789,5031,14486,43280,132777,420267,
%T A057151 1366307,4566966,15661086,55081118,198425478,731661754,2758808581,
%U A057151 10629386376,41814350148,167830018952,686822393793,2864024856054,12162059027416,52564545391789
%N A057151 Number of square binary matrices with n ones, with no zero rows or columns, up to row and column permutation.
%C A057151 Number of square binary matrices with n ones and with no zero rows or columns is A104602(n). - _Vladeta Jovovic_, Mar 25 2006
%C A057151 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
%H A057151 Max Alekseyev, <a href="/A057151/b057151.txt">Table of n, a(n) for n = 1..30</a>
%e A057151 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.
%e A057151 From _Gus Wiseman_, Nov 16 2018: (Start)
%e A057151 Non-isomorphic representatives of the a(1) = 1 through a(6) = 18 square set multipartitions:
%e A057151   {1}  {1}{2}  {2}{12}    {12}{12}      {1}{23}{23}      {12}{13}{23}
%e A057151                {1}{2}{3}  {1}{1}{23}    {2}{13}{23}      {1}{23}{123}
%e A057151                           {1}{3}{23}    {2}{3}{123}      {13}{23}{23}
%e A057151                           {1}{2}{3}{4}  {3}{13}{23}      {3}{23}{123}
%e A057151                                         {3}{3}{123}      {1}{1}{1}{234}
%e A057151                                         {1}{2}{2}{34}    {1}{1}{24}{34}
%e A057151                                         {1}{2}{4}{34}    {1}{1}{4}{234}
%e A057151                                         {1}{2}{3}{4}{5}  {1}{2}{34}{34}
%e A057151                                                          {1}{3}{24}{34}
%e A057151                                                          {1}{3}{4}{234}
%e A057151                                                          {1}{4}{24}{34}
%e A057151                                                          {1}{4}{4}{234}
%e A057151                                                          {2}{4}{12}{34}
%e A057151                                                          {3}{4}{12}{34}
%e A057151                                                          {4}{4}{12}{34}
%e A057151                                                          {1}{2}{3}{3}{45}
%e A057151                                                          {1}{2}{3}{5}{45}
%e A057151                                                          {1}{2}{3}{4}{5}{6}
%e A057151 (End)
%Y A057151 Cf. A049311, A056037, A056079, A056080, A057149, A057150, A057152.
%Y A057151 Cf. A054976, A101370, A104601, A104602, A120732, A283877, A319616.
%K A057151 nonn
%O A057151 1,3
%A A057151 _Vladeta Jovovic_, Aug 14 2000
%E A057151 More terms from _Max Alekseyev_, May 31 2007