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A086510
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Number of n X n real (0,1)-matrices with all eigenvalues >= 0.
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4
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OFFSET
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0,2
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LINKS
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EXAMPLE
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a(2)=13 because only 3 of the 16 possible matrices have eigenvalues < 0:
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0 1
1 0
with eigenvalues {1,-1}
and
1 1
1 0
.
0 1
1 1
both with eigenvalues {1.61803..(Golden ratio),-0.61803...}
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MATHEMATICA
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a[0] = 1; a[n_] := Module[{M, iter, cnt = 0}, M = Table[a[i, j], {i, 1, n}, {j, 1, n}]; iter = Thread[{Flatten[M], 0, 1}]; Do[If[AllTrue[Eigenvalues[ M], NonNegative], cnt++], Evaluate[Sequence @@ iter]]; cnt];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Frederique Oggier (frederique.oggier(AT)epfl.ch) and N. J. A. Sloane, Sep 10 2003
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EXTENSIONS
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STATUS
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approved
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