A087488 Number of n X n (-1,1)-matrices with all eigenvalues >= 0.

1, 1, 6, 64, 4744, 536736

Offset: 0

Author

Frederique Oggier (frederique.oggier(AT)epfl.ch) and N. J. A. Sloane, Oct 24 2003

Keywords

• nonn
• more
• hard

Examples

			For n = 2 the six matrices are (+ means +1, - means -1):
++ +- -- -+ +- ++
-- +- ++ -+ -+ ++
with eigenvalues
00 00 00 00 20 20 respectively.
		

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. A086510, A003024, A055165, A085656.

Programs

Mathematica

a[n_] := Select[Partition[#, n] & /@ Tuples[{-1, 1}, {n^2}], AllTrue[ Eigenvalues[#], NonNegative]&] // Length; a[0] = 1;
Do[Print[n, " ", a[n]], {n, 0, 5}] (* Jean-François Alcover, Feb 13 2019 *)

Extensions

a(5) from Jean-François Alcover, Feb 13 2019