# The Fibonacci Quarterly

## Basic Definitions and Formulas

The Fibonacci numbers F(n) and the Lucas numbers L(n) satisfy

F(n+2)=F(n+1)+F(n), F(0)=0, F(1)=1;

L(n+2)=L(n+1)+L(n), L(0)=2, L(1)=1.

Also, alpha=(1+sqrt 5)/2 and beta=(1-sqrt 5)/2, so that

F(n)=(alpha^n-beta^n)/(sqrt 5) and
L(n)=alpha^n+beta^n.
The Pell numbers P(n) and their associated numbers Q(n) satisfy

P(n+2)=2P(n+1)+P(n), P(0)=0, P(1)=1;

Q(n+2)=2Q(n+1)+Q(n), Q(0)=1, Q(1)=1.

If p=1+sqrt 2 and q=1-sqrt 2, then

P(n)=(p^n-q^n)/(sqrt 8) and Q(n)=(p^n+q^n)/2.

The Pell-Lucas numbers, R(n), are given by R(n)=2Q(n).

`Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, ...
Pell numbers: 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ...
`

## Submission Instructions

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