Artur grafix at csl.pl
Sun Jan 7 11:13:57 CET 2007

```Dear Peter and Seqfans,

I was analyzed all different characteristic polynomials of the binary
robust matrices 3 x 3
That results:
-1-x-x^2+x^3;S(3);6;(1,3),(1,2)
-1-2*x-x^2+x^3;S(3);6;(1,3),(1,2)
-1+2*x-3*x^2+x^3;S(3);6;(1,3),(1,2)
-1+x-2*x^2+x^3;S(3);6;(1,3),(1,2)

1-2*x-x^2+x^3;C(3)=A(3);3;(1,2,3)
1-x-2*x^2+x^3;C(3)=A(3);3;(1,2,3)

-1-3*x-x^2+x^3;reducible;2+1;(1+x)(-1-2x+x^2)
1-2*x^2+x^3;reducible;2+1,(-1+x)(-1-x+x^2)
-2+3*x-3x^2+x^3;reducible;2+1;(-2+x)(1-x+x^2)
1+x-3*x^2+x^3;reducible;(-1+x)(-1-2*x+x^2)

2-x-2*x^2+x^3;reducible;1+1+1;(-2 + x)(-1 + x)(1 + x)
-1+3*x-3*x^2+x^3;reducible;1+1+1;(-1+x)^3

Statistic:
C:2
S:4
R(2+1):4
R(1+1+1):2
Total Sum:12  Total reducible: 6

BEST WISHES
ARTUR

Brendan,
I'm updating A125587 with your two new terms,
and I'm correcting the definition of A006383 - thanks!

a(n) = number of inequivalent real invertible {0,1}-matrices
(where equivalence means that rows can be permuted
and columns can be permuted)
is in the OEIS.  The answer is that I don't know!

We also need:
b(n) = number of inequivalent real invertible {0,1}-matrices
(where equivalence means that rows can be permuted
and columns can be permuted, and the matrix can be transposed).

They both begin 1,2, but that's not much help!

It would be nice to have a few more terms of both!

Neil

Leroy reminds me that the question