A086510 Number of n X n real (0,1)-matrices with all eigenvalues >= 0.

1, 2, 13, 261, 15418, 2566333

Offset: 0

Author

Frederique Oggier (frederique.oggier(AT)epfl.ch) and N. J. A. Sloane, Sep 10 2003

Keywords

• nonn
• more

Examples

			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...}
		

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.
• Index entries for sequences related to binary matrices

Crossrefs

Cf. A003024, A055165, A085656, A098148.

Programs

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 *)

Extensions

a(5) from Hugo Pfoertner, Sep 26 2017