Certainly! You are describing Pascal's Triangle , a famous mathematical pattern discovered by Blaise Pascal. Here’s a detailed explanation:

Pascal's Triangle

Structure:

• Each row in Pascal’s Triangle starts and ends with the number 1.
• Every other number in the row is obtained by adding the two numbers directly above it from the previous row.

For example, the first few rows look like this:

      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1

How the numbers are formed:

• The number at position k in row n (both starting from 0) is the sum of the numbers at positions k-1 and k in row n-1.
• If there is no number at those positions (like at the edges), it is considered 0.

Sum of terms in each row:

• Another interesting pattern is that the sum of the numbers in each row is a power of 2.
• Specifically, the sum of the numbers in the nth row is 2n2^n2n.

For example:

• Row 0: 1 → sum = 1 = 202^020
• Row 1: 1 + 1 = 2 = 212^121
• Row 2: 1 + 2 + 1 = 4 = 222^222
• Row 3: 1 + 3 + 3 + 1 = 8 = 232^323

Summary:

• Pascal’s Triangle is a triangular array of numbers.
• Each number is the sum of the two numbers above it.
• Rows start and end with 1.
• The sum of the numbers in the nth row is 2n2^n2n.

If you want, I can also help you generate Pascal’s Triangle programmatically or explore more patterns related to it!