%I #25 Feb 14 2019 05:56:57
%S 1,1,6,64,4744,536736
%N Number of n X n (-1,1)-matrices with all eigenvalues >= 0.
%H B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, <a href="https://arxiv.org/abs/math/0310423">Acyclic digraphs and eigenvalues of (0,1)-matrices</a>, arXiv:math/0310423 [math.CO], 2003.
%H B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Sloane/sloane15.html">Acyclic digraphs and eigenvalues of (0,1)-matrices</a>, J. Integer Sequences, 7 (2004), #04.3.3.
%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%e For n = 2 the six matrices are (+ means +1, - means -1):
%e ++ +- -- -+ +- ++
%e -- +- ++ -+ -+ ++
%e with eigenvalues
%e 00 00 00 00 20 20 respectively.
%t a[n_] := Select[Partition[#, n] & /@ Tuples[{-1, 1}, {n^2}], AllTrue[ Eigenvalues[#], NonNegative]&] // Length; a[0] = 1;
%t Do[Print[n, " ", a[n]], {n, 0, 5}] (* _Jean-François Alcover_, Feb 13 2019 *)
%Y Cf. A086510, A003024, A055165, A085656.
%K nonn,more,hard
%O 0,3
%A Frederique Oggier (frederique.oggier(AT)epfl.ch) and _N. J. A. Sloane_, Oct 24 2003
%E a(5) from _Jean-François Alcover_, Feb 13 2019