Pascal's triangle in Python

In Pascal's triangle, each row starts and ends with 1, and every other number is the sum of the two numbers above it. Row 4 (counting the top row as row 0) is 1 4 6 4 1, because 1 + 3 = 4, 3 + 3 = 6 and 3 + 1 = 4.

The program

rows = int(input("Number of rows: "))

row = [1]
for _ in range(rows):
    print(" ".join(str(n) for n in row))
    middle = [row[j] + row[j + 1] for j in range(len(row) - 1)]
    row = [1] + middle + [1]

Typed in this example: 6. Press Run to type your own.

Number of rows: 6
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

How it works

• row holds the current row as a list. It starts as [1].
• After printing a row, the program builds the next one. row[j] + row[j + 1] adds each pair of neighbours. For [1, 3, 3, 1] the pairs give [4, 6, 4].
• Putting a 1 at each end gives the new row: [1, 4, 6, 4, 1].
• For row [1] there are no pairs, so middle is empty and the next row is [1, 1].

A centred triangle with math.comb()

The number in row i, position k (both counted from 0) is the number of ways to choose k items from i. math.comb(i, k) calculates it directly, so each value can be found without the row above it:

import math

rows = 5

lines = []
for i in range(rows):
    lines.append(" ".join(str(math.comb(i, k)) for k in range(i + 1)))

width = len(lines[-1])
for line in lines:
    print(line.center(width).rstrip())

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

• The program builds all the lines first, so it knows the width of the last one.
• line.center(width) adds spaces on both sides to centre the line. rstrip() removes the spaces on the right, which are not needed.
• Once the numbers have two or more digits (from row 5, with 10), the rows have different widths and the triangle shape becomes uneven.