The Square pyramidal number reference article from the English Wikipedia on 24-Apr-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

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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