Resol a_{n}=1/sqrt{5}(frac{1+sqrt{5}}{2})^n-1/sqrt{5}(frac{1-sqrt{5}}{2})^n

$$a _ { n } = \frac { 1 } { \sqrt { 5 } } ( \frac { 1 + \sqrt { 5 } } { 2 } ) ^ { n } - \frac { 1 } { \sqrt { 5 } } ( \frac { 1 - \sqrt { 5 } } { 2 } ) ^ { n }$$

Resoleu a_n

$$a_{n}=-\frac{\sqrt{5}\left(-\left(\frac{\sqrt{5}+1}{2}\right)^{n}+\left(\frac{1-\sqrt{5}}{2}\right)^{n}\right)}{5}$$

$$Denominator(n)\text{bmod}2=1$$