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 A276648 Number of points of norm <= n in the body-centered cubic lattice with the lattice parameter equal to 2/sqrt(3). 1

%I

%S 1,9,59,169,339,701,1243,1893,2741,3943,5577,7343,9409,12039,15065,

%T 18421,22227,26717,31879,37461,43655,50557,58071,66227,75121,85083,

%U 95801,107227,119541,133019,147271,161901,178127,195481,214143

%N Number of points of norm <= n in the body-centered cubic lattice with the lattice parameter equal to 2/sqrt(3).

%C Experimentally observed dense bcc clusters of gold contain 1, 9, 59, 169, 339, 701 and 1243 nanoparticles (N.G. Khlebtsov, Fig. 32 and text on p. 208), exactly matching the first 7 terms of the sequence.

%C First 5 terms are the same as A276450.

%H Yuriy Sibirmovsky, <a href="/A276648/b276648.txt">Table of n, a(n) for n = 0..50</a>

%H N. G. Khlebtsov, <a href="http://dx.doi.org/10.1016/j.jqsrt.2012.12.027">T-matrix method in plasmonics: An overview</a>, J. Quantitative Spectroscopy & Radiative Transfer 123 (2013) 184-217.

%e The origin has norm 0, thus a(0)=1. The distance to the 8 vertices of the cube from the origin is 1, because the edge of the cube is 2/sqrt(3). Thus a(1)=9.

%t DecM[A_]:=A[[1]]^2+A[[2]]^2+A[[3]]^2;

%t Do[N1=0;N2=0;

%t Do[A={l,k,j};

%t B={l+1/2,k+1/2,j+1/2};

%t If[DecM[A]<=3/4r^2,N1+=1];

%t If[DecM[B]<=3/4r^2,N2+=1],{l,-r-1,r+1},{k,-r-1,r+1},{j,-r-1,r+1}];

%t Print[r," ",N1+N2],{r,0,20}]

%Y Cf. A276450.

%K nonn

%O 0,2

%A _Yuriy Sibirmovsky_, Sep 11 2016

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Last modified September 17 12:41 EDT 2019. Contains 327131 sequences. (Running on oeis4.)