There are $m$ persons and $n$ chairs. Each person needs to maintain social distance between themselves and the person they are sitting next to. Therefore, once a person sits, the person who sits next to them sits at a distance that is in multiples of the integer $k$. We have to find the total number of arrangements possible so that all the people can be seated.
1.All the people must get a chair to sit on
2.Two arrangements are different either if the state of a chair is different in both cases or if two different people are seated on it. For example, for chairs $n=10$, person $m=2$, and $k=2$, if the first person sits at the 2nd position, then the second person can sit only at the 4th, 6th, 8th, or 10th position.
For example, $n=5,m=2,k=2$ no of arrangements possible are 4. (1,3) (1,5) (2,4) (3,5).
Can anyone suggest some approach to me for this combinatorics problem?