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A000410 Number of singular n X n rational (0,1)-matrices.
(Formerly M4308 N1803)
10
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) 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
REFERENCES
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
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.
FORMULA
n! * a(n) = A046747(n) - 2^(n^2) + n! * binomial(2^n -1, n).
CROSSREFS
Sequence in context: A162088 A199253 A199198 * A275686 A173760 A269882
KEYWORD
nonn,nice,more
AUTHOR
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 19 02:44 EDT 2024. Contains 370952 sequences. (Running on oeis4.)