In the question we have a cat in $(0,0)$. The cat can only go right or up. The cat wants to reach $(n,n)$, but must go through one of the points above $(x=y)$. Meaning a point $(k,k+1)$. Compute how many different ways can the cat reach (n,n)?
I realized I need to denote a step to the right by $0$ and a step up by $1$ and sum the valid sequences though I'm not sure how to do this.
A solution would be very appreciated!
Hint
Look up Catalan numbers (paths that never cross the diagonal)
You already know how to compute total paths.
What further do you need to do ?