I am solving an infinite horizon maximization problem, which yields as FOC second-order recurrence relation
$A_{n+1} = \delta A_{n+2} + \delta A_{n} + c_n$,
where $\{c_n\}_{n=0}^\infty$ and $\delta$ are exogenous (i.e. I need a solution for $A_n$ in terms of $\delta$ and $c_n$). Is there a textbook way of solving this that I missed (no maths major here, so entirely possible)? (I know how to solve this without the forcing term).
Thanks and Best wishes,
Leon