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Growth of a linear recurrent sequence

Consider the sequence defined by $a_0=a_1=1$ and $a_n=2a_{n-1}-3a_{n-2}$ for $n\geq 2$. This is the sequence https://oeis.org/A087455. I would like to prove that $|a_n|>100$ when $n>10$. How can we d …
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