Removal of K objects such that no two are adjacent

Question

There are $2$ rows joined side-by-side with $n$ objects in each row. What is the number of ways to remove exactly $k$ objects such that no two vacant places, after removal, are adjacent to each other?

For example, when $n=4$, $k=2$, the answer is $18$, and when $n=5$, $k=3$ the answer is $38$.

I'm not able to get a formula to solve it for any value of $n,k$ ($k \leq 2n$)

Answer 1

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