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:

$2, 2, 6, 14, 34, 82, 198, 478, 1154, \ldots$

This sequence is A002203 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

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

Source of Name

This entry was named for John Pell and François Édouard Anatole Lucas.

Sources

• Weisstein, Eric W. "Pell Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PellNumber.html