Start by writing down the given recurrence relation in a form suitable for generating functions, typically by multiplying both sides by \( x^n \) and summing over all \( n \).

Express the generating function \( G(x) \) in terms of itself by leveraging the recurrence relation, then isolate \( G(x) \) to find a closed-form expression.

Solve for the coefficients of \( G(x) \) by expanding it into a power series and interpreting the result in terms of the original recurrence.