Definition:Pell-Lucas Numbers

Definition
The Pell-Lucas numbers are a sequence $\left \langle {Q_n}\right \rangle$ which is formally defined by the recurrence relation:
 * $Q_n = \begin{cases} 2 & : n = 0 \\

2 & : n = 1 \\ 2 Q_{n - 1} + Q_{n - 2} & : \text {otherwise}\end{cases}$

The sequence of Pell-Lucas numbers begins:
 * $2, 2, 6, 14, 34, 82, 198, 478, 1154, \ldots$

Also known as
The Pell-Lucas numbers are also known as the companion Pell numbers.

Also see

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