Pell numbers

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The Pell numbers are defined by the recurrence relation $P_{n}=2P_{n-1}+P_{n-2}$, with $P_{0}=0$ and $P_{1}=1$. They can also be obtained with this formula: $P_{n}={\frac {(1+{\sqrt {2}})^{n}-(1-{\sqrt {2}})^{n}}{2{\sqrt {2}}}}$. See A000129.