22. Find the number of $n$-permutations with repetition, $N_{n}$, formed by $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}$ such that $a_{1}$ and $a_{3}$ both appear an even number of times.
22. $N_{n}=\frac{6^{n}+2 \cdot 4^{n}+2^{n}}{4}$.