Octagonal number

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, <math>O_n = n^2 + 2(n^2 – n)<math>.

Octagonal numbers consistently alternate parity.