primitive binary matrices?

[N. J. A. Sloane]

Would someone work out a few terms of the following
sequence?

It is probably not in the OEIS and it should be!

a(n) = number of real n X n primitive (0,1)-matrices A.

Primitive means that for some k, every element of A^k is
strictly positive.

It is known that you don't need to check values
of k bigger than n^2 - 2n + 2
(this is a theorem of Wielandt, that if A
is primitive then k <= n^2 - 2n + 2)

References - see A002522.

The asymptotics are studied in the book

 Sachkov, V. N.; Tarakanov, V. E. Combinatorics of nonnegative matrices. Translated from the 2000 Russian original by Valentin F. Kolchin. Translations of Mathematical Monographs, 213. American Mathematical Society, Providence, RI, 2002. x+269 pp. ISBN: 0-8218-2788-X (Reviewer: D. J. Hartfiel) 15-02 (15A48)

NJAS