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