Relation to Neibouring enemy question

This question is similar to enemy Question , only diff is there we were having “or” , here we have “and” . Why is it so that recursive relation is same in both the cases .

@deepak19.engg Catalan numbers is answer of many problems so you will see this recurrence in many problem, you will also see this recurrence when you try to find all possible bst.
Search Catalan Number and Wikipedia will show you that this number is answer to many problem
If this resolves your doubt mark it as resolved.