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 A086510 Number of n X n real (0,1)-matrices with all eigenvalues >= 0. 3
 1, 2, 13, 261, 15418, 2566333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices, arXiv:math/0310423 [math.CO], 2003. B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices, J. Integer Sequences, 7 (2004), #04.3.3. EXAMPLE a(2)=13 because only 3 of the 16 possible matrices have eigenvalues < 0: .   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...} MATHEMATICA 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]; Do[Print[n, " ", a[n]], {n, 0, 5}] (* Jean-François Alcover, Dec 09 2018 *) CROSSREFS Cf. A003024, A055165, A085656, A098148. Sequence in context: A276744 A042677 A134296 * A326360 A123113 A126742 Adjacent sequences:  A086507 A086508 A086509 * A086511 A086512 A086513 KEYWORD nonn,more AUTHOR Frederique Oggier (frederique.oggier(AT)epfl.ch) and N. J. A. Sloane, Sep 10 2003 EXTENSIONS a(5) from Hugo Pfoertner, Sep 26 2017 STATUS approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)