Sum of products of binomial coefficients.

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If $(1+x+x^2)^n= \Sigma_{r=0}^{2n}a_r x^r$ then $a_r- \binom n1 a_{r-1}+\binom n2 a_{r-2}-\binom n3 a_{r-3}+....+(-1)^r\binom nr a_{0} $ is equal to (r is not a multiple of 3)

Options

a)0

b) $^nC_r$

c) $a_r$

d)1

There's no way I can think of to get an expression like that. I tried differentiating to see whether it could help me or not but it was in vain. Please help me out of this problem.