HMMT November 2016 U31

Define a number to be an anti-palindrome if, when written in base 3 as $a_{n} a_{n-1} \ldots a_{0}$, then $a_{i}+a_{n-i}=$ 2 for any $0 \leq i \leq n$. Find the number of anti-palindromes less than $3^{12}$ such that no two consecutive digits in base 3 are equal.