Monsky's theorem states that it is impossible to dissect a square into an odd number of triangles of equal area. If $n$ is an even integer, I am interested in the number of ways of dissecting a square into $n$ such triangles. Call $s_n$ this number. My question is:
What are the first terms of the sequence $s_n$?
with an option on this other question:
How can we compute $s_n$ for a given $n$?
Judging from the lack of answers to this question, it does not seem trivial that these numbers are even finite, let alone known. Obviously, $s_2=2$, and I believe that $s_4=25$. Other values are unknown to me.
Added 15/05/2015: I believe that $s_6$ is at least (
and perhaps exactly) equal to $818$. This, however, does not lead to any sequence of the OEIS, so I'd be happy to be proved wrong.
Added 03/06/2015: For $n=2,4$ (but not for $n=6$, see mjqxxxx's answer below) the equidissections of the square that I could find all involve triangles whose vertices are rational numbers. For larger $n$, it is not sufficient to look only at equidissections satisfying this property.