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Octagonal Number

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OctagonalNumber

An octagonal number is a polygonal number of the form O_n=n(3n-2), where n is a positive integer. The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is

(x(5x+1))/((1-x)^3)=x+8x^2+21x^3+40x^4+...

for |x|<1.

See also

Octagonal Heptagonal Number, Octagonal Hexagonal Number, Octagonal Pentagonal Number, Octagonal Square Number, Octagonal Triangular Number

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References

Sloane, N. J. A. Sequence A000567/M4493 in "The On-Line Encyclopedia of Integer Sequences."

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Octagonal Number

Cite this as:

Weisstein, Eric W. "Octagonal Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OctagonalNumber.html

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