Q. about {0,1}-matrices.

[Artur]

Dear Neil,
If somebody will be write procedure for these sequence will be possible  
also count how many different characteristic polynomials have these 5 x 5  
robust matrices. Number of different characteristic polynomials will be  
much lower that a(5) because lot of that same matrices will be give that  
same characteristic polynomial (from definition with with free term  
different as zero).
ARTUR




Dnia 06-01-2007 o 03:47:54 N. J. A. Sloane <njas at research.att.com>  
napisał(a):

> Dear MathFun, SeqFans:
>
> Could anyone extend this sequence?
>
> %I A125587
> %S A125587 1,4,68,5008
> %N A125587 Call an n X n matrix robust if the top left i X i submatrix  
> is invertible for all i = 1...n. Sequence gives number of n X n robust  
> real {0,1}-matrices.
> %e A125587 a(2) = 4:
> %e A125587 10 10 11 11
> %e A125587 01 11 01 10
> %O A125587 1,2
> %Y A125587 Cf. A125586.
> %K A125587 nonn,more
> %A A125587 njas and Vinay Vaishampayan (vinay(AT)research.att.com), Jan  
> 05 2007
>
> This "robust" property is relevant when doing an LU decomposition
> of a matrix, so it may have a more official name (besides "all principal
> submatrices are nonsingular", I mean).
>
> Neil
>
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