Prove that the set of sequences satisfying relation $$P(n) u_n = Q(n) u_{n+1}$$ with $$P(X) = X(X-1)(X-2) \quad \text{and} \quad Q(X) = X(X-2)$$ is a vector space for which we will specify a basis and the dimension.
Prove that the set of sequences satisfying relation
$$P(n) u_n = Q(n) u_{n+1}$$
with
$$P(X) = X(X-1)(X-2) \quad \text{and} \quad Q(X) = X(X-2)$$
is a vector space for which we will specify a basis and the dimension.