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Pentagonal Pyramidal Number

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers is

(x(2x+1))/((x-1)^4)=x+6x^2+18x^3+40x^4+....

The odd pentagonal pyramidal numbers are given by 1, 75, 405, 1183, 2601, ... (OEIS A015223), having squares 1, 5625, 164025, ... (OEIS A014799), while the even pentagonal pyramidal numbers are given by 6, 18, 40, 126, 196, 288, ... (OEIS A015224), having squares 36, 324, 1600, 15876, ... (OEIS A014800).

See also

Pentagonal Number, Pyramidal Number

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References

Sloane, N. J. A. Sequences A002411/M4116, A014799, A014800, A015223, and A015224 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Pentagonal Pyramidal Number

Cite this as:

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

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