Robot Paths

Let’s say a robot is located at the top-left corner of an n x n grid. The robot can move either up, down, left, or right, one space at a time. It also cannot visit the same spot twice. The robot is trying to reach the bottom-right corner of the grid.

Write a function to count the number of ways that the robot can reach the bottom-right corner of the grid. Your function should receive n (the size of the grid) as a parameter.

A board can be generated using this function:

function makeBoard(n) {
  let board = [];
  for (let i = 0; i < n; i++) {
    board.push([]);
    for (let j = 0; j < n; j++) {
      board[i].push(false);
    }
  }
  board.toggle = (i, j) => {
    board[i][j] = !board[i][j];
  };
  board.hasBeenVisited = (i, j) => {
    return board[i][j];
  };
  return board;
}

Example

robotPaths(3) should create a 3 X 3 board, count the following paths, and return 12

S
1
2	3	E

S
1	4	5
2	3	E

S	5	6
1	4	7
2	3	E

S
1	2	3
		E

S	3	4
1	2	5
		E

S
1	2
	3	E

S	1	2
		3
		E

S	1	2
	4	3
	5	E

S	1	2
5	4	3
6	7	E

S	1
	2
	3	E

S	1
3	2
4	5	E

S	1
	2	3
		E