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Centered Pentagonal Number

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CenteredPentagonalNumber

A centered polygonal number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is (5n^2+5n+2)/2, and the first few such numbers are 1, 6, 16, 31, 51, 76, ... (OEIS A005891). The generating function of the centered pentagonal numbers is

(x^2+3x+1)/((1-x)^3)=1+6x+16x^2+31x^3+....

See also

Centered Polygonal Number, Centered Square Number, Centered Triangular Number, Hex Number, Pentagonal Number

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References

Sloane, N. J. A. Sequence A005891/M4112 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Centered Pentagonal Number

Cite this as:

Weisstein, Eric W. "Centered Pentagonal Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CenteredPentagonalNumber.html

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