Pascal's Triangle Generator: Any Row
Pascal's triangle generator builds the famous triangle of binomial coefficients up to 100 rows with exact big numbers. Every number is the sum of the two numbers above it, and row n lists the coefficients of (a + b) to the power n. Highlight odd or even numbers to reveal the Sierpinski triangle pattern, or mark any multiple to see divisibility patterns. You can also look up a single entry C(n, k), see the sum of each row, and download the triangle as a PNG picture or a text file.
Pascal's Triangle Generator
Generate Pascal's triangle up to 100 rows. Highlight odd, even or multiples, look up any binomial coefficient and download as PNG or text.
How to use the Pascal's Triangle Generator
- Enter how many rows you want, from 1 to 100.
- Choose a highlight: none, odd numbers, even numbers or multiples of a number.
- Use the lookup to find a single binomial coefficient C(n, k).
- Copy the triangle, or download it as text or PNG.
Features
- Up to 100 rows with exact big-integer values
- Highlight odd, even or multiples of any number
- Sierpinski triangle pattern from odd numbers
- Row sums that equal powers of 2
- Binomial coefficient lookup C(n, k)
- Download as PNG or text
Frequently asked questions
What is Pascal's triangle?
It is a triangle of numbers where each entry is the sum of the two entries directly above it. The edges are all 1. It was studied by Blaise Pascal, and was known much earlier in Persia, India and China.
How is Pascal's triangle used in binomial expansion?
Row n gives the coefficients of (a + b) raised to n. For example row 4 is 1, 4, 6, 4, 1, so (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4.
What is the sum of each row?
Row n (counting from 0) adds up to 2 to the power n. Row 0 is 1, row 1 is 2, row 2 is 4, row 3 is 8 and so on. The row sums are shown beside the triangle.
What pattern do the odd numbers make?
Highlight the odd numbers and the triangle shows a Sierpinski triangle, a fractal made of smaller and smaller triangles. Entry C(n, k) is odd exactly when k and n − k share no binary 1 digit.
How do I find a single entry such as C(10, 3)?
Type n and k into the lookup. Row 10, position 3 is 120. Rows and positions both start counting at 0.