An infinite grid with two rows is divided into unit squares. One of the cells in the second row is colored red and all other cells in the grid are white. Initially, we are in the red cell. In one move, we can move from one cell to an adjacent cell (sharing a side). Find the number of sequences of \( n \) moves such that no cell is visited more than once. (In particular, it is not allowed to return to the red cell after several moves.)
Problem
Source: XIII International Festival of Young Mathematicians Sozopol 2024, Theme for 10-12 grade
Tags: combinatorics