Search

The Online Encyclopedia and Dictionary
 
     
 

Encyclopedia

Dictionary

Quotes
 

Pell number

In mathematics, the Pell numbers and Companion Pell Numbers (Pell-Lucas Numbers) are both sequences of integers.

Pell numbers

The Pell numbers are defined recursively by:

F(n)= \left\{ \begin{matrix} 0\,,\qquad\qquad\qquad\quad\,\ \ \,&&\mbox{if }n=0\,;\ \ \\ 1,\qquad\qquad\qquad\qquad\,&&\mbox{if }n=1;\ \ \,\\ 2F(n-1)+F(n-2)&&\mbox{otherwise.} \end{matrix} \right.

In words: you start with 0 and 1, and then produce the next Pell number by adding twice the previous Pell number to the Pell number before that. The first few terms of the sequence are 0, 1, 2, 5, 12, 29, 70, 169, 408 ...

Companion Pell Numbers (Pell-Lucas Numbers)

The Companion Pell numbers are defined recursively by:

F(n)= \left\{ \begin{matrix} 2\,,\qquad\qquad\qquad\quad\,\ \ \,&&\mbox{if }n=0\,;\ \ \\ 2,\qquad\qquad\qquad\qquad\,&&\mbox{if }n=1;\ \ \,\\ 2F(n-1)+F(n-2)&&\mbox{otherwise.} \end{matrix} \right.

In words: you start with 2 and 2, and then produce the next Pell number by adding twice the previous Pell number to the Pell number before that. The first few terms of the sequence are 2, 2, 6, 14, 34, 82, 198 , 478 ...

The contents of this article are licensed from Wikipedia.org under the GNU Free Documentation License. How to see transparent copy
  
 
     
 
Arts and Culture Entertainment People Science Social Sciences Geography
Maths Nature Knowledge All Categories
Fact Archive.com, 2005. Legal info