I have found here {https://math.stackexchange.com/questions/2167885/compositions-of-n-into-odd-parts} that the number of integer compositions of n into k odd parts would be ${\frac{n+k-1}{2} \choose k-1}$.
I would like to find the number of integer compositions of n into k even parts. My guess is that it would be the same, but I do not see how to prove it.
Each positive, even number is at least equal to two, so you can subtract one to get an odd, but still positive, number.
Therefore, the number of ways to decompose $n$ into $k$ even numbers is the same as the number of compositions of $n-k$ into $k$ odd numbers; and for that you already have a formula.