%I #25 Apr 03 2020 11:32:00

%S 1,2,3,5,7,18,43,313,7525,846992,324127859,403254094631,

%T 1555631972009429,19731915624463099552,791773335030637885025287,

%U 107432353216118868234728540267,47049030539260648478475949282317451,71364337698829887974206671525372672234854

%N Number of equivalence classes of nonzero regular 0-1 matrices of order n.

%C Previous name was: Number of different row sums among Latin squares of order n.

%C A regular 0-1 matrix has all row sums and column sums equal. Equivalence is defined by independently permuting rows and columns (but not by transposing). - _Brendan McKay_, Nov 18 2015

%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>

%F a(n) = A333681(n-1). - _Andrew Howroyd_, Apr 03 2020

%e For n = 4, representatives of the a(4) = 5 classes are

%e [1 0 0 0] [1 1 0 0] [1 1 0 0] [1 1 1 0] [1 1 1 1]

%e [0 1 0 0] [1 1 0 0] [0 1 1 0] [1 1 0 1] [1 1 1 1]

%e [0 0 1 0] [0 0 1 1] [0 0 1 1] [1 0 1 1] [1 1 1 1]

%e [0 0 0 1] [0 0 1 1] [1 0 0 1] [0 1 1 1] [1 1 1 1].

%e G.f. = x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 18*x^6 + 43*x^7 + 313*x^8 + 7525*x^9 + ...

%Y One less than the row sums of A133687.

%Y Cf. A333681.

%K nonn

%O 1,2

%A Eric Rogoyski

%E Description changed, after discussion with Andrew Howroyd, by _Brendan McKay_, Nov 18 2015

%E Terms a(12) and beyond from _Andrew Howroyd_, Apr 03 2020