First time posting, so happy to hear feedback on how I can write a better question. My background in recursive equations is limited to solving linear recurring relations. I have a challenging problem that is quite different than that. Excuse my lack of familiarity with the lingo, I’ll try to best explain my issue in layman terms.
I’d appreciate any resources I could read up on to learn more about this kind of problem.
Suppose we have the following recursive equation:
$f(n) = \frac{37}{38}(1 + f(n-1)) + \frac{1}{38}(1 + f(n + 35)); f(0) = 0$
This seems to diminish asymptotically, but my knowledge is too limited to determine a solution for the asymptote or even to approximate the solution with code.
I began an attempt to approximate this with some code, but got stuck when I realized that this is circular. When $f(n+35)$ is being computed, it’ll eventually recursively reach my starting point and loop infinitely. For example, if I’m trying to approximate $f(2)$, it’ll call $f(37)$, then keep calling $f(36)$, $f(35)$, ...$f(2)$ and loop all over again.
I’d definitely appreciate any resources or suggestions for approximating this or even better, determining the asymptote for any value of $n$. If this is intractable, oh well, but I’d love to learn more about why.