If \( \left(1+x+x^{2}\right)^{n}=\sum_{r=0}^{2 n} a_{r} \cdot x^{r} \) then \( 6\left(a_{0}+a_{6}+a_{12}+a_{18}+\ldots.\right)= \)
a) \( 3^{n}-1+2^{n+1} \cos \frac{n \pi}{3} \)
b) \( 3^{n}+1+2^{n+1} \cdot \cos \frac{n \pi}{3} \)
c) \( 3^{n}-1+2^{n} \sin \frac{n \pi}{3} \)
d) \( 3^{n}+1+2^{n} \sin \frac{n \pi}{3} \)
