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 \(w+v+x+y+z\)?

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