[seqfan] Property of sequence A115281.

[Mats Granvik]

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