Question 74
Let $n \in \mathbb{N}$. Find the number of all sequences $A_0, A_1, \dots, A_n$ of pairwise different points in the plane with non-negative integer first coordinates and second coordinates $0$ or $1$, such that $A_0 = (0,0)$ and
$$
|x_{A_i} - x_{A_{i-1}}| + |y_{A_i} - y_{A_{i-1}}| = 1
$$
for $1 \le i \le n$.
$$
|x_{A_i} - x_{A_{i-1}}| + |y_{A_i} - y_{A_{i-1}}| = 1
$$
for $1 \le i \le n$.