A polygonal number of the form . The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is
Octagonal Number
See also
Octagonal Heptagonal Number, Octagonal Hexagonal Number, Octagonal Pentagonal Number, Octagonal Square Number, Octagonal Triangular NumberExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A000567/M4493 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Octagonal NumberCite this as:
Weisstein, Eric W. "Octagonal Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OctagonalNumber.html