A055165
Number of invertible n X n matrices with entries equal to 0 or 1.
Original entry on oeis.org
1, 1, 6, 174, 22560, 12514320, 28836612000, 270345669985440, 10160459763342013440
Offset: 0
Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000
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}}}.
- 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, arXiv:math/0511636 [math.CO], 2005; Linear Algebra and its Applications, 414 (2006), 310-346.
- Miodrag Zivkovic, Classification of (0,1) matrices of order not exceeding 8.
- Index entries for sequences related to binary matrices
A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = sequence
A002416.
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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
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from itertools import product
from sympy import Matrix
def A055165(n): return sum(1 for s in product([0,1],repeat=n**2) if Matrix(n,n,s).det() != 0) # Chai Wah Wu, Sep 24 2021
More terms from Miodrag Zivkovic (ezivkovm(AT)matf.bg.ac.rs), Feb 28 2006
A116532
Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct, up to permutation of rows.
Original entry on oeis.org
0, 0, 3, 285, 50820, 23551920, 31898503077, 134251404794199
Offset: 1
Binary matrices with distinct rows and columns, various versions:
A059202,
A088309,
A088310,
A088616,
A089673,
A089674,
A093466,
A094000,
A094223,
A116532,
A116539,
A181230,
A259763
A000410
Number of singular n X n rational (0,1)-matrices.
Original entry on oeis.org
0, 0, 6, 425, 65625, 27894671, 35716401889, 144866174953833
Offset: 1
- 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).
- 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
n=7 term from Guenter M. Ziegler (ziegler(AT)math.TU-Berlin.DE)
A116527
Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.
Original entry on oeis.org
0, 0, 0, 75, 22365, 13303500, 21058940420, 98692672142610
Offset: 1
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