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
It is pyramidal in shape.It has a lone pair.
It is a sequence in which the numbers represent the number of spheres in a pyramidal stack of spheres. There are a number of possible configurations for stacking spheres - a visit to fruit stalls may show you options. The square based pyramidal numbers are given by the sums of the first n square numbers. So U(1) = 1^1 = 1 U(2) = 1^2 + 2^2 = 1 + 4 = 5 and so on U(n) = 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6. However, there are also triangle based pyramidal numbers and hexagon based pyramidal numbers, since these configuration also give stable stacks.
Square pyramidal
Trigonal Pyramidal
square pyramidal