A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The th triangular number is the number of dots composing a triangle with dots on a side, and is equal to the sum of the  natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is:

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406 …