This (also) appears to be 3^(n-1) * (3^n - 1)/2.
VERY WILD surmise: It's the number of integer-sided
Heron triangles whose circumdiameter is the product
of n distinct primes of shape 4k + 1.
(3^n - 1)/2 of these are (believed to be) right
triangles, so that the number of non-right ones is
(3^(n-1) - 1) * (3^n - 1)/2
A003462 and a new(?) sequence 0, 8, 104, 1040, 9680, ...
R.