19.1 Problem

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

Take a look at Figure 8 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 that span a small square side length.

For the said problem there are exactly 6 paths (as depicted in Figure 8). 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.