Reach for the Summit - M-S3-A2

Algebra Level 4

A sequence $\{a_n\}$ is such that $a_1=1$ , $a_2=3$ , $a_3=6$ , and $\ a_n=3a_{n-1}-a_{n-2}-2a_{n-3}$ for $n \ge 4$ .

If $a_n>\lambda \times 2^{n-2}$ for all $n \ge 4$ , find the maximum integer value of $\lambda$ .