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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 $\lambda$.

Reach for the Summit problem set - Mathematics

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