Suppose we have a sequence $\{x_n\}_{n=1}^{\infty}$ which is defined by a recursive rule $x_n = g(x_1, x_2, ..., x_{n-1})$.
There are infinitely many explicit functions $f(n)$ which satisfy $f(n) = x_n,\, \forall n \in \mathbb{Z}$. Does this ever pose an issue when attempting to solve for $f(n)$? How come when we usually solve recurrence relations we can get "nice" solutions?