Commuting in Manhattan
A man walks \(n\) blocks north and \(n\) blocks west of his residence to get to work. As they are installing a sewage pipe diagonally across town, he can touch, but cannot cross over, the main diagonal line.
The above figure shows \(84\) possible paths he could take for \(n=5\).
How many possible routes can he take if \(n=28\)?