Pyramidal number
A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an r-sided polygon of points.[1] The term usually refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to pyramids with three or more sides.[2] It is possible to extend the pyramidal numbers to higher dimensions.
Formula
The formula for the nth r-gonal pyramidal number is
This formula can be factored:
where Tn is the nth triangular number.
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See also
- Triangular pyramidal number (three sides)
- Square pyramidal number (four sides)
- Pentagonal pyramidal number (five sides)
- Hexagonal pyramidal number (six sides)
- Heptagonal pyramidal number (seven sides)
References
- Weisstein, Eric W. "Pyramidal Number". MathWorld.
- Sloane, N. J. A. (ed.). "Sequence A002414". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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