A possible candidate for OEIS

[Brendan McKay]

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.

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