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 A055165 Number of invertible n X n matrices with entries equal to 0 or 1. 19
 1, 6, 174, 22560, 12514320, 28836612000, 270345669985440, 10160459763342013440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All eigenvalues are nonzero. LINKS Eric Weisstein's World of Mathematics, Nonsingular Matrix. Chai Wah Wu, Can machine learning identify interesting mathematics? An exploration using empirically observed laws, arXiv:1805.07431 [cs.LG], 2018. Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346. Miodrag Zivkovic, Classification of (0,1) matrices of order not exceeding 8. FORMULA For an asymptotic estimate see A046747. A002884 is a lower bound. A002416 is an upper bound. a(n) = n! * A088389(n). - Gerald McGarvey, Oct 20 2007 EXAMPLE For n=2 the 6 matrices are {{{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{1, 0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}, {{1, 1}, {1, 0}}}. PROG (PARI) a(n)=sum(t=0, 2^n^2-1, !!matdet(matrix(n, n, i, j, (t>>(i*n+j-n-1))%2))) \\ Charles R Greathouse IV, Feb 09 2016 CROSSREFS Cf. A056990, A056989, A046747, A055165, A002416, A003024 (positive definite matrices). A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = sequence A002416. Sequence in context: A323279 A214801 A233225 * A318538 A071095 A134632 Adjacent sequences:  A055162 A055163 A055164 * A055166 A055167 A055168 KEYWORD nonn,nice,hard,more AUTHOR Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000 EXTENSIONS More terms from Miodrag Zivkovic (ezivkovm(AT)matf.bg.ac.rs), Feb 28 2006 Description improved by Jeffrey Shallit, Feb 17 2016 STATUS approved

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Last modified September 21 12:13 EDT 2020. Contains 337271 sequences. (Running on oeis4.)