[seqfan] Re: Property of sequence A115281.
Robert Israel
israel at math.ubc.ca
Wed Jul 7 23:00:47 CEST 2010
I don't know if there's a specific name, but if J is
0 0 0 0 0 -i
0 0 0 0 i 0
0 0 0 -i 0 0
0 0 i 0 0 0
0 -i 0 0 0 0
i 0 0 0 0 0
your property can be written as J.A.J = A^(-1). This
says that J.A is an involution.
Robert Israel israel at math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
On Wed, 7 Jul 2010, Mats Granvik wrote:
> Hi,
>
> Consider the lower triangular matrix T(n,k):
> 1 0 0 0 0 0
> 2 1 0 0 0 0
> 2 2 1 0 0 0
> 2 2 2 1 0 0
> 2 2 2 2 1 0
> 2 2 2 2 2 1
> defined by: if n = k then 1 elseif n>k then 2 else 0.
>
> Multiply it with its transpose:
> 1 2 2 2 2 2
> 0 1 2 2 2 2
> 0 0 1 2 2 2
> 0 0 0 1 2 2
> 0 0 0 0 1 2
> 0 0 0 0 0 1
>
> So that you get:
> 1 2 2 2 2 2
> 2 5 6 6 6 6
> 2 6 9 10 10 10
> 2 6 10 13 14 14
> 2 6 10 14 17 18
> 2 6 10 14 18 21
>
> Which appears to be triangle A115281 seen as a square array.
> This array has the property that the matrix inverse is the
> same array reversed and signed:
> 21 -18 14 -10 6 -2
> -18 17 -14 10 -6 2
> 14 -14 13 -10 6 -2
> -10 10 -10 9 -6 2
> 6 -6 6 -6 5 -2
> -2 2 -2 2 -2 1
>
> Is there a name for an array with that property?
>
> Regards,
> Mats Granvik
>
>
>
>
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