I have to solve several recurrence equations originating from physical problems, and I am looking for some references where techniques for different types of equations are collected.
Most of my equations, in addition to linear terms, contain products of the form $f(n+k)f(n)$, with $k$ being $-1,0,1$ or $2$ (depending on the example I have).
I am interested both in cases when $f$ is defined on $\mathbb{N}$ or some finite set with specified "boundary conditions".
I will be grateful for any suggestion.