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A127502
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Number of n X n positive definite matrices with 1's on the main diagonal and -1's and 0's elsewhere.
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2
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OFFSET
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1,2
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COMMENTS
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A real matrix M is positive-definite if x M x' > 0 for all nonzero real vectors x. Equivalently, all eigenvalues of M + M' are positive.
M need not be symmetric. For the number of different values of M + M' see A084552.
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LINKS
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Table of n, a(n) for n=1..10.
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EXAMPLE
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For n = 2 the three matrices are {{{1, 0}, {0, 1}}, {{1, 0}, {-1, 1}}, {{1, -1}, {0, 1}}}.
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PROG
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(PARI) { a(n) = M=matrix(n, n, i, j, 2*(i==j)); r=0; b(1); r } { b(k) = local(t); if(k> n, t=0; for(i=1, n, for(j=1, i-1, if(M[i, j]==1, t++); )); r+=2^t; return; ); forvec(x=vector(k-1, i, [ -1, 0]), for(i=1, k-1, M[k, i]=M[i, k]=x[i]); if( matdet(vecextract(M, 2^k-1, 2^k-1), 1)>0, b(k+1) ) ) } (Alekseyev)
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CROSSREFS
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Cf. A085656, A085657, A085658, A086215, A038379, A080858, A083029, A127503.
Sequence in context: A123681 A007151 A195895 * A175176 A208897 A027546
Adjacent sequences: A127499 A127500 A127501 * A127503 A127504 A127505
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KEYWORD
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nonn,nice
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AUTHOR
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Max Alekseyev, Jan 16 2007
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STATUS
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approved
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