The sequence ($\displaystyle {L}_{{n}}$) is generated using the Fibonacci recursion rule $\displaystyle {L}_{{{n}+{1}}}={L}_{{n}}+{L}_{{{n}-{1}}}$. However, the initial conditions (the seeds) are different from the Fibonacci sequence. In this case, $\displaystyle {L}_{{0}}={1}$ and $\displaystyle {L}_{{1}}={7}$.

What are the next five values in this sequence?
$\displaystyle {L}_{{2}}$ =
$\displaystyle {L}_{{3}}$ =
$\displaystyle {L}_{{4}}$ =
$\displaystyle {L}_{{5}}$ =
$\displaystyle {L}_{{6}}$ =