Find the 101st term!

Probability Level 3

Consider the recurrence relation $a_n = 2a_{n-1} + 3 a_{n-2} + 3^n$ for $n \geq 2$ with initial conditions $a_0 = -1, a_1 = 1.$

Given that $a_{100}$ is in the form of

$\LARGE \frac {x\cdot y^z - w}{v}$

where $x,y,w,z$ are prime numbers and $v$ as a perfect square, what is the value of $w+v+x+y+z$ ?