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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
OFFSET
0,2
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, 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.
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
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