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.

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