Rhombic Dodecahedral Number
المؤلف:
Conway, J. H. and Guy, R. K.
المصدر:
The Book of Numbers. New York: Springer-Verlag
الجزء والصفحة:
...
24-12-2020
961
Rhombic Dodecahedral Number
A figurate number which is constructed as a centered cube with a square pyramid appended to each face,
where 
is a centered cube number and 
is a square pyramidal number. The first few are 1, 15, 65, 175, 369, 671, ... (OEIS A005917). The generating function of the rhombic dodecahedral numbers is
 |
(3)
|
A related set of numbers is the number of cubes in the Haűy construction of the rhombic dodecahedron, given by
 |
(4)
|
for 
an odd number. Re-indexing with 
then gives
 |
(5)
|
giving the first few values 1, 33, 185, 553, 1233, ... (OEIS A046142).
REFERENCES:
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 53-54, 1996.
Sloane, N. J. A. Sequences A005917/M4968 and A046142 in "The On-Line Encyclopedia of Integer Sequences."
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