Artur grafix at csl.pl
Sun Jan 7 00:46:51 CET 2007

```Dear Neil and Seqfans,
5 x 5 number of robust a(5)=1603232
Number of binary matrices which aren't robust a(5)=31951200

My procedure was count 2564096 determinants 5 x 5 but these algorhithm
probably isn't effective method for higher n

I'm not sending to all sequans that we will check that Ferenc will receive
that same result. If yes I'm agree that will be coauthor of a(5)
ARTUR

Dnia 06-01-2007 o 23:07:52 Edwin Clark <eclark at math.usf.edu> napisał(a):

> On Sat, 6 Jan 2007, Ferenc Adorjan wrote:
>
>> Hello Neil and Seqfans,
>>
>> I have composed a Pari program to determine the number of nxn robust
>> 0,1 matrices.
>> Certainly, the program below is neither optimal nor verfied. It
>> provides properly the value of 4 and 68, but as the fourth term it
>> Somebody should verify the program (or the term #4) before anybody
>> tries to calculate the fifth term.
>> Ferenc
>>
>
>
> I wrote a Maple program to calculate nxn robust matrices. It
> agrees with the values 1, 4, 68, 5008 given by Neil. It is
> now using those 5008 of size 4x4 to compute the number of
> 5x5's. At the present rate it should be done in about 5 more
> hours.
>
> --Edwin
>
>
>
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Brendan said:

In a little less than 30 minutes, my C program counted:

Did your C program use the following observation:

For going from n=6 to n=7 that's a potential saving
of 6! * 6!.  In other words, for each of the 2224232640
6x6s, put it into canonical form.
When you have all the canon. forms, and their multiplicities,
then see how many ways each can be extended.
But you are the Latin square expert, so probably you did this
without thinking it was worth mentioning.

Neil

```