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.