pascal's triangle is a triangular matrix whose top is 1, which is regarded as (row0). there are two 1s in column 1 (row1) (1&1). these two 1s are the sum of the left and right numbers above them (numbers not within the triangle are considered 0). and so on to generate the second column (row2): 0+1=1; 1+1=2; 1+0=1. column 3 (row3): 0+1=1; 1+2=3; 2+1=3; 1+0=1. following this method, the following columns can be produced.