PUMaC 2011 Algebra B Problem 7

A sequence of real numbers \{a_n\}_{n \geq 1} has the following property:
6 a_n+5 a_{n-2}=20+11 a_{n-1} \text { (for } n \geq 3 \text { ). }
The first two elements are a_1=0, a_2=1. Find the integer closest to a_{2011}.