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A085506 Number of {-1,0,1} n X n matrices that have (real and) positive eigenvalues. 2
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: A114474 A344395 A280305 * A307084 A132508 A215218
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 March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)