This is a sawn-down version of a puzzle "Arranging cats and dogs" that Matt Parker recently posted on YouTube.
In our version we have a pair of cats, and eight cushions. We want to seat each cat on its own cushion, with the restriction that they cannot occupy adjacent cushions, in case they start a cat fight. Here is one possible arrangement.
You see the cats are not next to one another, so the rule is satisfied.
The question is: how many possible arrangements are there? What if there were 9 cushions? Or 10? Can you give a general formula?