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A000410
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Number of singular n X n rational (0,1)-matrices.
(Formerly M4308 N1803)
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10
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OFFSET
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1,3
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..8.
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
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FORMULA
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n! * a(n) = A046747(n) - 2^(n^2) + n! * binomial(2^n -1, n).
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CROSSREFS
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Cf. A000409, A046747, A064230, A064231.
Sequence in context: A162088 A199253 A199198 * A275686 A173760 A269882
Adjacent sequences: A000407 A000408 A000409 * A000411 A000412 A000413
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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n=7 term from Guenter M. Ziegler (ziegler(AT)math.TU-Berlin.DE)
a(8) from Vladeta Jovovic, Mar 28 2006
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STATUS
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approved
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