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A055165
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Number of invertible n X n matrices with entries equal to 0 or 1.
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20
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OFFSET
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0,3
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COMMENTS
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All eigenvalues are nonzero.
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LINKS
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FORMULA
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EXAMPLE
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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}}}.
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PROG
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(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
(Python)
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
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CROSSREFS
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A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = sequence A002416.
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000
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EXTENSIONS
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More terms from Miodrag Zivkovic (ezivkovm(AT)matf.bg.ac.rs), Feb 28 2006
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STATUS
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approved
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