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A000410 Number of singular n X n rational (0,1)-matrices.
(Formerly M4308 N1803)
11
0, 0, 6, 425, 65625, 27894671, 35716401889, 144866174953833 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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, Apr 03 2006

REFERENCES

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

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).

LINKS

Table of n, a(n) for n=1..8.

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

CROSSREFS

Cf. A000409, A046747, A064230, A064231.

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

Sequence in context: A162088 A199253 A199198 * A275686 A173760 A269882

Adjacent sequences:  A000407 A000408 A000409 * A000411 A000412 A000413

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

a(8) from Vladeta Jovovic, Mar 28 2006

STATUS

approved

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Last modified March 27 08:32 EDT 2017. Contains 284146 sequences.