Fibonacci-ish

I have a squence similar to the Fibonacci sequence

$${a}{\left({\mathtt{n}}\right)} = {\mathtt{3}}{\mathtt{\,\times\,}}\left({a}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{a}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{\mathtt{\,-\,}}{a}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}\right)$$

And I know that the Fibonacci sequence could be reduced to

Can the first sequence be reduced similarly to the fibonachi sequence