Definition:Pell Numbers

Definition
The Pell numbers are a sequence $\left \langle {P_n}\right \rangle$ 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:
 * $0, 1, 2, 5, 12, 29, 70, 169, 408, 985, \ldots$

Also see

 * Definition:Pell-Lucas Numbers
 * Sequence of Best Rational Approximations to Square Root of 2