31.1 Problem

This exercise was inspired by the following Euler Project problem, but it was modified by me.

Take a look at Figure 15 below. You will find a big square build of 2x2 smaller squares. Your task is to start at the top left corner of the big square and go to the bottom right corner of it using only right and down arrows (as few as possible) that span a small square side length.

For the said problem there are exactly 6 paths (as depicted in Figure 15). But think about a big square composed of 3x3 little squares.

How many different paths are there? Can you draw these paths? Well, use Julia to find out.