Anupam and Raja

Recently Anupam was working with a function defined as follows: The function takes an integer $N$ as argument. Suppose there are $N$ people sitting in a circular queue numbered $1$ to $N$. The function returns the number of ways we can select a subset of them such that no $2$ selected people are adjacent to each other. Rajarshi heard of this function, and made the following problem: You a