An octagonal number is a figurate number that represents an octagon. The octagonal number for n is given by the formula 3n2 - 2n, with n > 0. The first few octagonal numbers are
1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936
The octagonal number for n can also be calculated by adding the square of n to twice the n-1th heteromecic number, or, to put it algebraically, On = n2 + 2(n2 - n).
Octagonal numbers consistently alternate parity.