The first few triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78. They were given their name by the ancient Greeks, who noticed that a number of dots equal to one of these numbers could be arranged in a triangular pattern.

Triangular numbers have many interesting properties. For example, all
the triangular numbers can be found in the second diagonal (counting from
zero; the third diagonal if you start at one) of
Pascal's Triangle. All odd square numbers are
1 more than 8 times a triangular number. For example, 9 = 1 + 8 x 1,
25 = 1 + 8 x 3, and so on. The formula for the n^{th} triangular number is ^{n(n+1)}/_{2}.