

A005874


Theta series of hexagonal closepacking 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 closepacked spherical clusters, J. Chem. Phys. 83 (1985) 65206534.


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



