Triangular numbers

A triangular number is a figurate number: a number that can be represented by a regular geometric arrangement of equally spaced points. Triangular numbers can be thought of as the numbers of dots you need to make a triangle:

The triangular numbers are found in the third diagonal of Pascal's triangle:

             1                Row 0
           1   1              Row 1
         1   2   1            Row 2
        1  3   3  1           Row 3
       1  4  6  4   1         Row 4
     1  5  10  10  5 1        Row 5
    1  6  15  20  15 6 1      Row 6
  1  7  21  35 35  21 7 1     Row 7
1  8  28  56 70  56  28  8  1 Row 8    

The numbers in red colour are triangular numbers.