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A000519
Number of equivalence classes of nonzero regular 0-1 matrices of order n.
3
1, 2, 3, 5, 7, 18, 43, 313, 7525, 846992, 324127859, 403254094631, 1555631972009429, 19731915624463099552, 791773335030637885025287, 107432353216118868234728540267, 47049030539260648478475949282317451, 71364337698829887974206671525372672234854
OFFSET
1,2
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
FORMULA
a(n) = A333681(n-1). - Andrew Howroyd, Apr 03 2020
EXAMPLE
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 + ...
CROSSREFS
One less than the row sums of A133687.
Cf. A333681.
Sequence in context: A048417 A071710 A048403 * A088732 A336446 A129693
KEYWORD
nonn
AUTHOR
Eric Rogoyski
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
STATUS
approved