2008 AMC 10B Problem 11

Suppose that (u_n) is a sequence of real numbers satisfying u_{n+2}=2u_{n+1}+u_n,

and that u_3=9 and u_6=128. What is u_5?

\mathrm{(A)}\ 40\qquad\mathrm{(B)}\ 53\qquad\mathrm{(C)}\ 68\qquad\mathrm{(D)}\ 88\qquad\mathrm{(E)}\ 104

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.