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 A085506 Number of {-1,0,1} n X n matrices that have (real and) positive eigenvalues. 1
 1, 5, 133, 18905 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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, J. Integer Sequences, 7 (2004), #04.3.3. 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. Eric Weisstein's World of Mathematics, Positive Definite Matrix MATHEMATICA a[n_] := Module[{M, iter, cnt = 0}, M = Table[a[i, j], {i, 1, n}, {j, 1, n}]; iter = Thread[{Flatten[M], -1, 1}]; Do[If[AllTrue[Eigenvalues[M], If[Im[#] != 0, False, Positive[#]]&], cnt++], Evaluate[Sequence @@ iter]]; cnt]; Do[Print[n, " ", a[n]], {n, 1, 3}] (* Jean-François Alcover, Dec 09 2018 *) CROSSREFS Sequence in context: A296191 A114474 A280305 * A307084 A132508 A215218 Adjacent sequences:  A085503 A085504 A085505 * A085507 A085508 A085509 KEYWORD nonn,more AUTHOR Eric W. Weisstein, Jul 02 2003 EXTENSIONS Offset corrected by Max Alekseyev, Oct 18 2008 STATUS approved

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Last modified October 21 04:40 EDT 2019. Contains 328291 sequences. (Running on oeis4.)