1,3

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

a(n) = 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 (vladeta(AT)Eunet.yu), Apr 03 2006

N. Metropolis and P. R. Stein, On a class of (0,1) matrices with vanishing determinants, J. Combin. Theory, 3 (1967), 191-198.

M. 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.

A046747(n) = 2^(n^2) - n! * binomial(2^n -1, n) + n! * A000410(n). Cf. A000409.

Adjacent sequences: A000407 A000408 A000409 this_sequence A000411 A000412 A000413

Sequence in context: A000474 A029591 A106206 this_sequence A028665 A001328 A051735

nonn,nice,more

njas

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

a(8) from Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 28 2006