I might be wrong, but for the NVE ensemble, T(n)=s^n * T(n=0) can be derived directly from |v|(n)=q^n * |v|(n=0) if we write:
T(n) = (Σ[k=0→K] |v_k(n)|^2)/(3k(K-m)) = (Σ[k=0→K] |q^n v_k(0)|^2)/(3k(K-m)) = q^n T(0)
So I should then be able to use T(n)=s^n * T(n=0) to find the value of s. But when I tried this earlier, I got much different results. That's why I just wanted to make sure my understanding of n in T(n) is correct.
In another case I am using a 20 fs time step and 1000 steps, equating to 20 ps. Is n still an element of [0,1000]?