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A085506 Number of {-1,0,1} n X n matrices that have (real and) positive eigenvalues. 1

%I

%S 1,5,133,18905

%N Number of {-1,0,1} n X n matrices that have (real and) positive eigenvalues.

%H B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Sloane/sloane15.html">Acyclic digraphs and eigenvalues of (0,1)-matrices</a>, J. Integer Sequences, 7 (2004), #04.3.3.

%H B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, <a href="http://arXiv.org/abs/math.CO/0310423">Acyclic digraphs and eigenvalues of (0,1)-matrices</a>, arXiv:math/0310423 [math.CO], 2003.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PositiveDefiniteMatrix.html">Positive Definite Matrix</a>

%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>

%t 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];

%t Do[Print[n, " ", a[n]], {n, 1, 3}] (* _Jean-Fran├žois Alcover_, Dec 09 2018 *)

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Jul 02 2003

%E Offset corrected by _Max Alekseyev_, Oct 18 2008

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)