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sage: import sympy
sage: sympy.rsolve?

gives :

Signature:      sympy.rsolve(f, y, init=None)
Docstring:     
   Solve univariate recurrence with rational coefficients.

   Given k-th order linear recurrence \operatorname{L} y = f, or
   equivalently:

      a_{k}(n) y(n+k) + a_{k-1}(n) y(n+k-1) + ... + a_{0}(n) y(n) =
      f(n)

   where a_{i}(n), for i=0, ..., k, are polynomials or rational
   functions in n, and f is a hypergeometric function or a sum of a
   fixed number of pairwise dissimilar hypergeometric terms in n,
   finds all solutions or returns "None", if none were found.

[ Abbreviated... ]

HTH,

sage: import sympy
 sage: sympy.rsolve?

gives :

Signature:      sympy.rsolve(f, y, init=None)
Docstring:     
   Solve univariate recurrence with rational coefficients.

   Given k-th order linear recurrence \operatorname{L} y = f, or
   equivalently:

      a_{k}(n) y(n+k) + a_{k-1}(n) y(n+k-1) + ... + a_{0}(n) y(n) =
      f(n)

   where a_{i}(n), for i=0, ..., k, are polynomials or rational
   functions in n, and f is a hypergeometric function or a sum of a
   fixed number of pairwise dissimilar hypergeometric terms in n,
   finds all solutions or returns "None", if none were found.

[ Abbreviated... ]

Of course, see also Wikipedia...

HTH,