The 2 x n seating derangements

Abstract

Abstract In this paper, we study the derangement of 2n persons sitting 2 rows and n columns. In how many ways can the persons rearrange their seating in accordance with the following condition. Each seat is located by one person and reoccupied by another person and each person moves to a horizontal or a vertical or a diagonal neighboring seat. We establish the system of recurrence relations for the solution of this problem and provide the solution of the system of recurrence relations.