

A086510


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


3




OFFSET

0,2


LINKS

Table of n, a(n) for n=0..5.
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


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}] (* JeanFrançois Alcover, Dec 09 2018 *)


CROSSREFS

Cf. A003024, A055165, A085656, A098148.
Sequence in context: A276744 A042677 A134296 * A326360 A123113 A126742
Adjacent sequences: A086507 A086508 A086509 * A086511 A086512 A086513


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



