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What are pyramidal numbers?

Updated: 12/22/2022
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10y ago

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In mathematics, a pyramid number, or square pyramidal number, is a number that represents the number of stacked spheres in a pyramid with a square base.

The first few square pyramidal numbers are:

1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819

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A pyramid is a solid shape with a polygon base and triangular faces that meet at an apex. The base need not be a square as is often assumed in many of the answers here.

For a pyramid with a base that is a polygon with r sides where r is an integer greater than 2, the nth pyramidal numbe is:

P(r, n) = [(3n2 + n3*(r-2) - n(r - 5)]/6

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