If $\left(1+x+x^2\right)^n=a_0+a_1 x+a_2 x^2+\ldots+a_{2 n} x^{2 n}$, then $a_0+a_2+a_4+\ldots+a_{2 n}=$

• A

  $3^n$
• B

  $3^n+1$
• C

  $\frac{3^n-1}{2}$
• Correct answer
  D

  $\frac{3^n+1}{2}$

Hence, the correct answer is option: 'D'.