A possible candidate for OEIS

[Antti Karttunen]

Brendan McKay wrote:

>Equivalently, directed graphs (simple but loops allowed) without a
>few small forbidden subgraphs (those allowing 2 distinct paths of
>length 2 from vertex x to vertex y for some x,y; I think there are
>6 possibilities).  Nice.
>
>  
>
Nice interpretation! For those SeqFanaticians for whom the above 
connection seems entirely mysterious,
please read this: http://mathworld.wolfram.com/AdjacencyMatrix.html
and it should be clear. BTW, the differences in mathematical knowledge 
and skills
on this list are surely huge, so why not to let people to have a possibility
to learn a bit each time there is a concrete sequence or other example
which makes it possible?

Yours,

Antti

>One can also consider isomorphism classes of those digraphs.
>
>A question: what is the maximum number of 1s in such a matrix?
>
>Brendan.
>
>* Dan Dima <dimad72 at gmail.com> [060821 07:02]:
>  
>
>>Hi all,
>>
>>I search through OEIS but I did not find any sequence corresponding to the
>>following:
>>
>>"A binary matrix is a matrix whose entries are all either 0 or 1. How many
>>n?n binary matrices A are there such that A*^2* is also a binary matrix? "
>>
>>a(n) - n?n binary matrices A such that A*^2* is a binary matrix
>>
>>a(1) = 2
>>a(2) = 11
>>a(3) = 172
>> a(4) = 6327
>>a(5) = 474286
>>a(6) = 67147431
>>.....
>>
>>Best regards,
>>Dan Dima
>>    
>>
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