Dominant Eigenvalue

\[ x_{n+2} = 1 - x_{n+1} + 6 x_{n} \]

A sequence is generated by the recurrence relation as described above with \( x_{0}= x_{1} = 0 \). Determine

\[\displaystyle\lim_{n \to \infty} \frac{x_{n+1}}{x_n}.\]

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