We let and , and make a triangle by for natural numbers with and . Then we get the following Figure 5.

If we calculate each , then we get the following Figure 6.

One of the authors (Matsui) studied the least nonnegative residues of numbers in Figure 6 taken modulo 2, and he got the following Figure 7. He is a freshman in a high school, and he did not know the Sierpinski Gasket. Therefore his discovery shows an amazing possibility of young students.

After he discovered Figure 7, he colored 1,0 with different colours. In the next section you can see many beautiful pictures made from these Pascal like triangles.