Pascal's Triangle and Its Relatives

Background

Simplest Example

Pascal's triangle is familiar from the study of algebra and combinatorics.

Though sometimes presented as an equilateral triangle, for our purposes a right isosceles format is better.

Make a triangular array of boxes and fill each box of the left and right sides with 1s.

Starting from the top, fill every other box with the sum of the entries in the box immediately above, and immediately above and to the left.

Here are the first few rows.

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