Find the 101st term!

Probability Level 3

Consider the recurrence relation an=2an1+3an2+3n a_n = 2a_{n-1} + 3 a_{n-2} + 3^n for n2n \geq 2 with initial conditions a0=1,a1=1.a_0 = -1, a_1 = 1.

Given that a100a_{100} is in the form of

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

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


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