I am searching for the number of odd coefficients of
$\qquad (x^4 + x^3 + x^2 + x + 1)^n$
for arbitrary $n$.
It took some hours to compute the result for $n=12207$. There are $16333$ odd coefficients.
I need to compute it for $n=27637$ as well. I tried
Total[CoefficientList[(x^4 + x^3 + x^2 + x + 1)^27637, x, Modulus -> 2]]
but it is too slow.
Are there faster ways to do it?