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| A '''pyramidal number''' is a [[figurate number]] that represents a [[pyramid]] with a [[Polygonal number|polygonal]] base and a given number of [[Triangular number|triangular]] sides. The term is most often used to refer to [[square pyramidal number]]s, which have a [[square]] base with four sides, but it can also refer to:
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| *[[Tetrahedral number|Triangular pyramidal number]] (three sides)
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| *[[Square pyramidal number]] (four sides)
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| *[[Pentagonal pyramidal number]] (five sides)
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| *[[Hexagonal pyramidal number]] (six sides)
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| *[[Heptagonal pyramidal number]] (seven sides)
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| as well as to pyramids with higher numbers of sides <ref>http://oeis.org/A002414</ref>
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| The formula for a ''r''-gonal pyramid number is:
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| :<math>P_n^r= \frac{3n^2 + n^3(r-2) - n(r-5)}{6}</math>
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| r ∈ [[ℕ]], r ≥ 3
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| This formula factors to:
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| :<math>\begin{align}
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| P_n^r&=\frac{n(n+1)[n(r-2)-(r-5)]}{(2)(3)}\\
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| &=\left(\frac{n(n+1)}{2}\right)\left(\frac{n(r-2)-(r-5)}{3}\right)\\
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| &=T_n\ \left(\frac{n(r-2)-(r-5)}{3}\right)\\
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| \end{align}</math>
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| == References ==
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| <references />
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| [[Category:Figurate numbers]]
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Revision as of 20:28, 21 February 2014
Landscape Gardener Dapolito from Mahone Bay, enjoys to spend time pyrotechnics, Telecharger Clash of Clans Hack and tombstone rubbing. Gets plenty of encouragement from life by touring places like Botanical Garden (Orto Botanico).
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