One of the most interesting Number Patterns is Pascal’s Triangle. The Name “Pascal’s Triangle” named after Blaise Pascal, a famous French Mathematician and Philosopher.
In Mathematics, Pascal’s Triangle is a triangular array of binomial coefficients.The rows of Pascal’s triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows.
The triangle is constructed in the below manner:
For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.
Equation to generate each entry in Pascal triangle:
for any non-negative integer n and any integer k between 0 and n, inclusive. This recurrence for the binomial coefficients is known as Pascal’s rule. Pascal’s triangle has higher dimensional generalizations. The three-dimensional version is called Pascal’s pyramid or Pascal’s tetrahedron, while the general versions are called Pascal’s simplices.
Example of Pascal’s Triangle: