A005874 - OEIS

%I M2236 #42 Jun 20 2022 13:14:14

%S 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,

%T 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,

%U 0,36,24,6,12,12,3,24,12,6,0,24,0,24,6,12,0,48,12

%N Theta series of hexagonal close-packing with respect to triangle between tetrahedra.

%C Just take the theta series for the h.c.p. and subtract the coordinates of the center of the triangle from each point. - _N. J. A. Sloane_, May 18 2021

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

%H Andrey Zabolotskiy, <a href="/A005874/b005874.txt">Table of n, a(n) for n = 0..1000</a>

%H S. K. K. Choi, A. V. Kumchev and R. Osburn, <a href="http://arxiv.org/abs/math/0502007">On sums of three squares</a>, arXiv:math/0502007 [math.NT], 2005.

%H N. J. A. Sloane and B. K. Teo, <a href="http://dx.doi.org/10.1063/1.449551">Theta series and magic numbers for close-packed spherical clusters</a>, J. Chem. Phys. 83 (1985) 6520-6534.

%F Sum_{n<=x} a(n)^2 ~ (8*Pi^4/(21*zeta(3))) * x^2. (Choi/Kumchev/Osburn) [Corrected by _Vaclav Kotesovec_, Oct 25 2015]

%Y Cf. A004012, A005872, A005873, A005889, A005890.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(63) and beyond from _Andrey Zabolotskiy_, Jun 20 2022