Consider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below.
Write a function to count the legal paths for an nxn grid. Return the count as a string. Check the last test for banned functions.
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