# Lucas numbers

The Lucas numbers are a slight variation of Fibonacci numbers. These numbers follow the same recursion:

 $l_{n+1}=l_{n}+l_{n-1}$

but having different initial conditions: $l_{1}=1,l_{2}=3$ leading to the sequence $1,3,4,7,11,18,29,47,76,123,\ldots$.

Lucas numbers have the following property: $l_{n}=f_{n-1}+f_{n+1}$ where $f_{n}$ is the $n^{th}$ Fibonacci number.

Title Lucas numbers LucasNumbers 2013-03-22 12:19:58 2013-03-22 12:19:58 Mathprof (13753) Mathprof (13753) 8 Mathprof (13753) Definition msc 11B39 Lucas sequence FibonacciSequence