# Seductive Recursive Sequences

Algebra Level 3

$$(\alpha_n)$$ and $$(\beta_n)$$ are two sequences defined recursively as $$\alpha_n=2 \alpha_{n-1}+1$$ and $$\beta_n=8 \beta_{n-1}+1$$ with $$\alpha_0=\beta_0=0.$$ Find the ratio

$\frac{\alpha_{2016}}{\beta_{672}}.$

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