[seqfan] Re: seq needed of (0,+-1) matrices

[Max Alekseyev]

The first 6 terms of the requested sequence are:

1, 3, 27, 125, 461, 1583

I may also get a(7) soon.

Regards,
Max

On Wed, Jan 18, 2012 at 1:16 PM, N. J. A. Sloane <njas at research.att.com> wrote:
>
> Dear Seq Fans, This paper:
>
> MR2002770 (2004g:05108)
> Wesp, Gerhard(A-SALZ-IM)
> A note on the spectra of certain skew-symmetric {1,0,1}-matrices. (English summary)
> Discrete Math. 258 (2002), no. 1-3, 339-346.
>
> discusses matrices A = (a_ij) of size nxn with entries from {-1,0,+1}
> which are skew-symmetric and have the additional property that
>
> a_wx a_yz + a_wy a_zx + a_wz a_xy = a_wx a_wy a_wz a_xy a_xz a_yz ... (*)
>
> for all distinct w,x,y,z in {1..n}.
>
> But he does not count them. Can someone compute the first few terms?
> Obviously a(1)=1 (the zero matrix),
> a(2) = 3, a(3) = 27 (up to this point we get all skew-symmetric matrices)
> and a(4) < 3^6
>
> (There seem to be several combinatorial applications)
>
> Neil
>
>
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