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Date: 26-6-2020
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Date: 27-10-2020
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Date: 8-1-2020
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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
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(1) |
The first few cases are therefore
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(2) |
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(3) |
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(4) |
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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