A Figurate Number corresponding to a configuration of points which form a pyramid with -sided Regular
Polygon bases can be thought of as a generalized pyramidal number, and has the form

(1) |

(2) | |||

(3) | |||

(4) |

so corresponds to a Tetrahedral Number , and to a Square Pyramidal Number .

The pyramidal numbers can also be generalized to 4-D and higher dimensions (Sloane and Plouffe 1995).

**References**

Conway, J. H. and Guy, R. K. ``Tetrahedral Numbers'' and ``Square Pyramidal Numbers''
*The Book of Numbers.* New York: Springer-Verlag, pp. 44-49, 1996.

Sloane, N. J. A. and Plouffe, S. ``Pyramidal Numbers.'' Extended entry for sequence M3382 in
*The Encyclopedia of Integer Sequences.* San Diego, CA: Academic Press, 1995.

© 1996-9

1999-05-26