The sequence ($\displaystyle {w}_{{n}}$) is generated using a recursion rule similar to the Fibonacci $\displaystyle {w}_{{{n}+{1}}}={2}\cdot{w}_{{n}}+{w}_{{{n}-{1}}}$. Notice that the coefficients in the recurssion rule are not all equal to 1. The initial conditions for this sequence are $\displaystyle {w}_{{0}}={0}$ and $\displaystyle {w}_{{1}}={3}$.

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