Solution of a_k x_{n-k}+...+a_0 x_n=0 is x_n = sum c_i lambda_i^n with lambda_i roots of characteristic polynomial; Fibonacci satisfies x_n=x_{n-1}+x_{n-2} with golden-ratio root.
Solution of a_k x_{n-k}+...+a_0 x_n=0 is x_n = sum c_i lambda_i^n with lambda_i roots of characteristic polynomial; Fibonacci satisfies x_n=x_{n-1}+x_{n-2} with golden-ratio root.