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.