# Recurrence relation with random number?

I got:

$$a_{n+2}+4a_{n+1}+a_{n}-2f(n+2)-4f(n+1)=0$$

We can arbitrary set $$a_{1}$$ and $$a_{2}$$.

And we don’t know what a formula $$f(x)$$ represents, but always know the return value of it. Please consider it as a sort of black boxes which gives us a random number corresponding to x.

And, at last, I want the general term of the sequence $$a_{n}$$. Or whether it just can be solved or not.

I know how to solve when the f(x) is a constant or a polynomial, but not this one.