Pyramidal Number
المؤلف:
Conway, J. H. and Guy, R. K.
المصدر:
"Tetrahedral Numbers" and "Square Pyramidal Numbers" The Book of Numbers. New York: Springer-Verlag,
الجزء والصفحة:
...
24-12-2020
1283
Pyramidal Number
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
![P_n^((r))=1/6n(n+1)[(r-2)n+(5-r)].](https://mathworld.wolfram.com/images/equations/PyramidalNumber/NumberedEquation1.gif) |
(1)
|
The first few cases are therefore
so 
corresponds to a tetrahedral number 
, and 
to a square pyramidal number 
.
The pyramidal numbers can also be generalized to four dimensions 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.
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