Square pyramidal number

From Biocrawler, the free encyclopedia.

A pyramidal number, or square pyramidal number, is a figurate number that represents a pyramid with a base and four sides. The nth pyramidal number is

that is, it is the sum of the squares of the first n integers.

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.

The sum of two consecutive square pyramidal numbers is an octahedral number.

See also: tetrahedral numberfr:Nombre pyramidal carré sl:Kvadratno piramidno število

Wikipedia (http://en.wikipedia.org/wiki/Main_Page) Square_pyramidal_number (http://en.wikipedia.org/wiki/Square_pyramidal_number) version history (http://en.wikipedia.org/w/index.php?title=Square_pyramidal_number&action=history) GNU Free Documentation Lizenz (http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License) CC-by-sa (http://creativecommons.org/licenses/by-sa/2.5/)

---