A054976 Number of binary n X n matrices with no zero rows or columns, up to row and column permutation.

1, 3, 17, 179, 3835, 200082, 29610804, 13702979132, 20677458750966, 103609939177198046, 1745061194503344181714, 99860890306900024150675406, 19611238933283757244479826044874, 13340750149227624084760722122669739026, 31706433098827528779057124372265863803044450

Offset

1,2

Comments

Also the number of non-isomorphic set multipartitions (multisets of sets) with n parts and n vertices. - Gus Wiseman, Nov 18 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Formula

a(n) = A002724(n) - 2*A002725(n-1) + A002724(n-1).

Example

From Gus Wiseman, Nov 18 2018: (Start)
Inequivalent representatives of the a(3) = 17 matrices:
  100 100 100 100 100 010 010 001 001 001 001 110 101 101 011 011 111
  100 010 001 011 011 001 101 001 101 011 111 101 011 011 011 111 111
  011 001 011 011 111 111 011 111 011 111 111 011 011 111 111 111 111
Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 set multipartitions:
  {{1}}  {{1},{2}}      {{1},{2},{3}}
         {{2},{1,2}}    {{1},{1},{2,3}}
         {{1,2},{1,2}}  {{1},{3},{2,3}}
                        {{1},{2,3},{2,3}}
                        {{2},{1,3},{2,3}}
                        {{2},{3},{1,2,3}}
                        {{3},{1,3},{2,3}}
                        {{3},{3},{1,2,3}}
                        {{1,2},{1,3},{2,3}}
                        {{1},{2,3},{1,2,3}}
                        {{1,3},{2,3},{2,3}}
                        {{3},{2,3},{1,2,3}}
                        {{1,3},{2,3},{1,2,3}}
                        {{2,3},{2,3},{1,2,3}}
                        {{3},{1,2,3},{1,2,3}}
                        {{2,3},{1,2,3},{1,2,3}}
                        {{1,2,3},{1,2,3},{1,2,3}}
(End)

Mathematica

A002724 = Cases[Import["https://oeis.org/A002724/b002724.txt", "Table"], {_, _}][[All, 2]];
A002725 = Cases[Import["https://oeis.org/A002725/b002725.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A002724[[n + 1]] - 2 A002725[[n]] + A002724[[n]];
a /@ Range[1, 13] (* Jean-François Alcover, Sep 14 2019 *)

Crossrefs

Column sums of A057150.

Cf. A007716, A048291 (labeled), A049311, A057149, A057151, A104601, A104602, A319616, A320808.

Sequence in context: A053934 A159592 A126443 * A304863 A163886 A340881

Adjacent sequences: A054973 A054974 A054975 * A054977 A054978 A054979

Keyword

easy,nonn

Author

Vladeta Jovovic, May 27 2000

Extensions

More terms from David Wasserman, Mar 06 2002

Terms a(14) and beyond from Andrew Howroyd, Apr 11 2020

Status

approved