Square pyramidal number

A square pyramidal number is a Nombre illustrated which represents a Pyramide with a base and four sides. N ième pyramidal number square is

$\backslash \; sum\_\; \{k=1\}\; ^nk^2=\; \{1\; \backslash \; over\; 6\}\; N\; (N\; +\; 1)\; (2n\; +\; 1)$

The first square pyramidal small numbers are:

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

The square pyramidal numbers can be modelled in physical space with a given number of balls and a square form which maintains the square of balls forming the base, i.e. N ². Except 1, there exists only another number which is at the same time square and pyramidal square, 4900. This result was proven by G.N. Watson in 1918.

The nap of two consecutive square pyramidal numbers forms a octahedral Nombre.

See too

• tetrahedral Number

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