 Octagonal number

The polygonal number $P_{8,n}=n(3n-2)$ for a positive integer $n$.

An octagonal number is a type of figurate number that represents a regular octagon. The \( n \)-th octagonal number can be calculated using the formula: \[ O_n = n(3n - 2) \] where \( O_n \) is the \( n \)-th octagonal number and \( n \) is a positive integer (1, 2, 3, ...).