Definition:Pell Numbers
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Definition
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:
- $0, 1, 2, 5, 12, 29, 70, 169, 408, 985, \ldots$
This sequence is A000129 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Also see
Source of Name
This entry was named for John Pell.
Sources
- Weisstein, Eric W. "Pell Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PellNumber.html