MathDB

There are

n

people seated on a circular table that have seats numerated from 1 to

n

clockwise. Let

k

be a fix integer with

2 \leq k \leq n

. The people can change their seats. There are two types of moves permitted:
1. Each person moves to the next seat clockwise. 2. Only the ones in seats 1 and

k

exchange their seats.
Determine, in function of

n

and

k

, the number of possible configurations of people in the table that can be attain by using a sequence of permitted moves.

Problem Statement