I have the following complexity equation: $T(n)=T(n-i)+T(n-(\frac{n}{m}-i))$ with the base case $T(m)=1$.
Is it possible to calculate a big $O$ approximation for such equation? What is the right method to do so?
Edit: I actually need to calculate this equation for any $1\leq{i}<\frac{n}{m}$ so if it is easier to consider $i$ as a constant, such a solution is also helpful.
Edit 2: I think the equation is also missing floor value of $\frac{n}{m}$ so it will be coherent