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Search: id:A127502
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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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+0
3
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| 1, 3, 19, 201, 3001, 55291, 1115003, 21837649, 373215601, 8282131891
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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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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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PROGRAM
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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: A001832 A123681 A007151 this_sequence A027546 A108993 A052886
Adjacent sequences: A127499 A127500 A127501 this_sequence 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 (maxale(AT)gmail.com), Jan 16 2007
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