Lucas numbersLucasNumbers2002-02-15 01:29:012006-09-01 09:13:12DefinitionThe \emph{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.