This article needs additional citations for verification. (October 2013) (Learn how and when to remove this template message)
Octagonal numbers can be formed by placing triangular numbers on the four sides of a square. To put it algebraically, the n-th octagonal number is
The octagonal number for n can also be calculated by adding the square of n to twice the (n - 1)th pronic number.
Octagonal numbers consistently alternate parity.
Sum of reciprocals
Test for octagonal numbers
Solving the formula for the n-th octagonal number, for n gives
An arbitrary number x can be checked for octagonality by putting it in this equation. If n is an integer, then x is the n-th octagonal number. If n is not an integer, then x is not octagonal.
- Deza, Elena; Deza, Michel (2012), Figurate Numbers, World Scientific, p. 57, ISBN 9789814355483.
- Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers
|This number article is a stub. You can help Wikipedia by expanding it.|