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A005874 Theta series of hexagonal close-packing with respect to triangle between tetrahedra.
(Formerly M2236)
1
0, 3, 2, 0, 3, 12, 0, 6, 0, 6, 0, 12, 6, 6, 12, 12, 3, 0, 2, 6, 0, 24, 0, 24, 6, 3, 0, 24, 6, 12, 12, 6, 0, 12, 0, 0, 18, 6, 12, 48, 0, 24, 0, 6, 0, 36, 0, 0, 6, 9, 14, 24, 6, 12, 12, 0, 0, 48, 0, 36, 24, 6, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..62.

S. K. K. Choi, A. V. Kumchev and R. Osburn, On sums of three squares, arXiv:math/0502007 [math.NT], 2005.

N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.

FORMULA

Sum_{n<=x} a(n)^2 ~ (8*Pi^4/(21*zeta(3))) * x^2. (Choi/Kumchev/Osburn)

CROSSREFS

Sequence in context: A131732 A198826 A088161 * A275622 A129239 A224825

Adjacent sequences:  A005871 A005872 A005873 * A005875 A005876 A005877

KEYWORD

nonn,easy,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Formula corrected by Vaclav Kotesovec, Oct 25 2015

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)