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 A086510 Number of n X n real (0,1)-matrices with all eigenvalues >= 0. 4
 1, 2, 13, 261, 15418, 2566333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..5. 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. Index entries for sequences related to binary matrices 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: A042677 A338424 A134296 * A356493 A334089 A326360 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 1 18:51 EST 2023. Contains 367502 sequences. (Running on oeis4.)