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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 Cf. A000409, A046747, A064230, A064231. Sequence in context: A162088 A199253 A199198 * A275686 A173760 A269882 Adjacent sequences: A000407 A000408 A000409 * A000411 A000412 A000413 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 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)