It is given that there are n seats for some event.
It is not know how many people attend from Group A or Group B.
But no two people from Group B should not sit together.
Like if there is 2 seats in event.
Valid combinations: AA AB BA
Invalid combinations: BB
What will be the number of valid combinations?
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $n\geq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form $$a_n=\ldots\quad,$$ whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $\ldots$