I have a function $F(t)$ defined as follows: $$F_{n}(t) = Q(F_{n-1}(t))$$ With the following definitions: $$F_0(t) = t$$ $$Q(t) = W(t \bmod H) + \frac{t}{H}$$ $W$ and $H$ are constant parameters. $W$, $H$ and $t$ are all integers.
I am having a difficult time coming up with an explicit definition of $F_n(t)$ that is not recurrent. I am not sure how to deal with the modulo operation in $Q(t)$. I've noticed that $F(t)$ is periodic, with the period being some function of $W$ and $H$ that looks very random.
Any ideas?