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

1, 5, 133, 18905

Offset

1,2

Links

Table of n, a(n) for n=1..4.

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

Index entries for sequences related to binary matrices

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: A114474 A344395 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