Pascal's Triangle and Its Relatives

Exercises

Pascal's triangles for other polynomials

2. Pascal's triangles for (1 + x + x²)(1 + x)ⁿ. We shade the boxes containing numbers congruent to

1 (mod 2)	1 or 2 (mod 3)

On a scale larger than the effect of the original polynomial (three boxes), these pictures appear similar to those of (1 + x)ⁿ.

This is not surprising, because in both this and the standard Pascal's triangle, the growth of the polynomials is determined by powers of (1 + x).

Return to Other polynomials Exercises.