# Find the 101st term!

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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