A116507 -id:A116507 - cp's OEIS frontend

A000410 Number of singular n X n rational (0,1)-matrices.

0, 0, 6, 425, 65625, 27894671, 35716401889, 144866174953833

Offset: 1

Number of all n X n (0,1)-matrices having distinct, nonzero ordered rows and determinant 0 - compare A000409.

a(n) is the number of singular n X n rational {0,1}-matrices with no zero rows and with all rows distinct, up to permutation of rows and so a(n) = binomial(2^n-1,n) - A088389(n). Cf. A116506, A116507, A116527, A116532. - Vladeta Jovovic, Apr 03 2006

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. Metropolis and P. R. Stein, On a class of (0,1) matrices with vanishing determinants, J. Combin. Theory, 3 (1967), 191-198.
Miodrag Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.
Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.
Index entries for sequences related to binary matrices

Cf. A000409, A046747, A064230, A064231.

n! * a(n) = A046747(n) - 2^(n^2) + n! * binomial(2^n -1, n).

n=7 term from Guenter M. Ziegler (ziegler(AT)math.TU-Berlin.DE)

a(8) from Vladeta Jovovic, Mar 28 2006

A116506 Number of singular n X n rational {0,1}-matrices with no zero rows.

Original entry on oeis.org

0, 3, 169, 28065, 16114831, 33686890209, 262530190180063, 7717643584470877185

Offset: 1

Vladeta Jovovic, Apr 03 2006

Cf. A000410, A116507, A116527, A116532.

a(n) = A055601(n) - A055165(n).

A116527 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.

Original entry on oeis.org

0, 0, 0, 75, 22365, 13303500, 21058940420, 98692672142610

Offset: 1

Vladeta Jovovic, Apr 03 2006

Cf. A000409, A000410, A116506, A116507, A116532.

a(n) = A094000(n) - A088389(n).

Conjecture: a(n) = A000410(n) - A000409(n-1) for n>1. - Jean-François Alcover, Jan 08 2020

cp's OEIS Frontend

A000410 Number of singular n X n rational (0,1)-matrices.

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A116506 Number of singular n X n rational {0,1}-matrices with no zero rows.

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A116527 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.

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