A000519 Number of equivalence classes of nonzero regular 0-1 matrices of order n.

1, 2, 3, 5, 7, 18, 43, 313, 7525, 846992, 324127859, 403254094631, 1555631972009429, 19731915624463099552, 791773335030637885025287, 107432353216118868234728540267, 47049030539260648478475949282317451, 71364337698829887974206671525372672234854

Offset: 1

Author

Eric Rogoyski

Keywords

• nonn

Comments

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

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

Examples

			For n = 4, representatives of the a(4) = 5 classes are
[1 0 0 0]  [1 1 0 0]  [1 1 0 0]  [1 1 1 0]  [1 1 1 1]
[0 1 0 0]  [1 1 0 0]  [0 1 1 0]  [1 1 0 1]  [1 1 1 1]
[0 0 1 0]  [0 0 1 1]  [0 0 1 1]  [1 0 1 1]  [1 1 1 1]
[0 0 0 1]  [0 0 1 1]  [1 0 0 1]  [0 1 1 1]  [1 1 1 1].
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 + ...
		

Links

• Index entries for sequences related to Latin squares and rectangles

Crossrefs

One less than the row sums of A133687.

Cf. A333681.

Formula

a(n) = A333681(n-1). - Andrew Howroyd, Apr 03 2020

Extensions

Description changed, after discussion with Andrew Howroyd, by Brendan McKay, Nov 18 2015

Terms a(12) and beyond from Andrew Howroyd, Apr 03 2020