\begin{definition}[Definition:Pell Numbers]
The '''Pell numbers''' are a sequence $\sequence {P_n}$ which is formally defined by the recurrence relation:
:$P_n = \begin{cases} 0 & : n = 0 \\
1 & : n = 1 \\
2 P_{n - 1} + P_{n - 2} & : \text {otherwise}\end{cases}$
The sequence of '''Pell numbers''' begins:
:$0, 1, 2, 5, 12, 29, 70, 169, 408, 985, \ldots$
{{OEIS|A000129}}
\end{definition}