Lucas number

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Lucas numbers is a series such that $L_1=1,L_2=3,L_n=L_{n-1}+L_{n-2},$ where $L_n$ is the $n^\text{th}$ number of Lucas numbers.

Lucas numbers is $\lfloor \phi^n \rfloor=L_n,$ where $n>1,n$ belongs to $\mathbb{N},\phi=\frac{1+\sqrt{5}}{2},$ and $L_n$ is the $n^\text{th}$ number.