Simplify $$\sum\_{k=0} \binom{n−2k} k$$ Or alternatively, show that it can't be simplified any more.

I tried Hockey stick identity but I had issues with the fact that the top had a -2k term. I then tried using $\binom {n+1}{k+1}$ = $\binom{n}{k} + \binom{n}{k+1}$, but again the -2k term means you can't add consecutive terms. Some values I calculated are

3 for n=4

4 for n=5

6 for n =6

9 for n=7.

There doesn't seem to be a pattern.