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

%I A054976 #20 Nov 20 2023 09:16:08
%S A054976 1,3,17,179,3835,200082,29610804,13702979132,20677458750966,
%T A054976 103609939177198046,1745061194503344181714,99860890306900024150675406,
%U A054976 19611238933283757244479826044874,13340750149227624084760722122669739026,31706433098827528779057124372265863803044450
%N A054976 Number of binary n X n matrices with no zero rows or columns, up to row and column permutation.
%C A054976 Also the number of non-isomorphic set multipartitions (multisets of sets) with n parts and n vertices. - _Gus Wiseman_, Nov 18 2018
%H A054976 Andrew Howroyd, <a href="/A054976/b054976.txt">Table of n, a(n) for n = 1..50</a>
%F A054976 a(n) = A002724(n) - 2*A002725(n-1) + A002724(n-1).
%e A054976 From _Gus Wiseman_, Nov 18 2018: (Start)
%e A054976 Inequivalent representatives of the a(3) = 17 matrices:
%e A054976   100 100 100 100 100 010 010 001 001 001 001 110 101 101 011 011 111
%e A054976   100 010 001 011 011 001 101 001 101 011 111 101 011 011 011 111 111
%e A054976   011 001 011 011 111 111 011 111 011 111 111 011 011 111 111 111 111
%e A054976 Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 set multipartitions:
%e A054976   {{1}}  {{1},{2}}      {{1},{2},{3}}
%e A054976          {{2},{1,2}}    {{1},{1},{2,3}}
%e A054976          {{1,2},{1,2}}  {{1},{3},{2,3}}
%e A054976                         {{1},{2,3},{2,3}}
%e A054976                         {{2},{1,3},{2,3}}
%e A054976                         {{2},{3},{1,2,3}}
%e A054976                         {{3},{1,3},{2,3}}
%e A054976                         {{3},{3},{1,2,3}}
%e A054976                         {{1,2},{1,3},{2,3}}
%e A054976                         {{1},{2,3},{1,2,3}}
%e A054976                         {{1,3},{2,3},{2,3}}
%e A054976                         {{3},{2,3},{1,2,3}}
%e A054976                         {{1,3},{2,3},{1,2,3}}
%e A054976                         {{2,3},{2,3},{1,2,3}}
%e A054976                         {{3},{1,2,3},{1,2,3}}
%e A054976                         {{2,3},{1,2,3},{1,2,3}}
%e A054976                         {{1,2,3},{1,2,3},{1,2,3}}
%e A054976 (End)
%t A054976 A002724 = Cases[Import["https://oeis.org/A002724/b002724.txt", "Table"], {_, _}][[All, 2]];
%t A054976 A002725 = Cases[Import["https://oeis.org/A002725/b002725.txt", "Table"], {_, _}][[All, 2]];
%t A054976 a[n_] := A002724[[n + 1]] - 2 A002725[[n]] + A002724[[n]];
%t A054976 a /@ Range[1, 13] (* _Jean-François Alcover_, Sep 14 2019 *)
%Y A054976 Column sums of A057150.
%Y A054976 Cf. A007716, A048291 (labeled), A049311, A057149, A057151, A104601, A104602, A319616, A320808.
%K A054976 easy,nonn
%O A054976 1,2
%A A054976 _Vladeta Jovovic_, May 27 2000
%E A054976 More terms from _David Wasserman_, Mar 06 2002
%E A054976 Terms a(14) and beyond from _Andrew Howroyd_, Apr 11 2020