2016/040) Derive the identity $u_{n+3} = 3u_{n+1} - u_{n-1}$ where $u_n$ is the $n^{th}$ fibonacci number and $n >= 2$

$u_{n+3} = u_{n+2} + u_{n+1}$
$= u_{n+1} + u_{n} + u_{n+1}$
$= 2u_{n+1} + u_{n}$
$= 2u_{n+1} + u_{n+1} - u_{n-1}$
$= 3 u_{n+1} -  u_{n-1}$