The Square pyramidal number reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Square pyramidal number

A pyramidal number, or square pyramidal number, is a figurate number that represents a pyramid with a base and four sides. The pyramidal number for n is given by the formula

They can also be computed by adding up the squares of the integers from 1 to n.

The first few pyramidal numbers are

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

Pyramidal numbers can be modelled in physical space with a given number of balls and a square frame that hold in place the number of balls forming the base, that is, n². Besides 1, there is only one other number that is both a square and a pyramidal number, 4900. This fact was proven by G.N. Watson in 1918.

See also: tetrahedral number

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