cp's OEIS Frontend

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

%I A276648 #25 Oct 04 2016 13:33:36
%S A276648 1,9,59,169,339,701,1243,1893,2741,3943,5577,7343,9409,12039,15065,
%T A276648 18421,22227,26717,31879,37461,43655,50557,58071,66227,75121,85083,
%U A276648 95801,107227,119541,133019,147271,161901,178127,195481,214143
%N A276648 Number of points of norm <= n in the body-centered cubic lattice with the lattice parameter equal to 2/sqrt(3).
%C A276648 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 A276648 First 5 terms are the same as A276450.
%H A276648 Yuriy Sibirmovsky, <a href="/A276648/b276648.txt">Table of n, a(n) for n = 0..50</a>
%H A276648 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 A276648 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 A276648 DecM[A_]:=A[[1]]^2+A[[2]]^2+A[[3]]^2;
%t A276648 Do[N1=0;N2=0;
%t A276648 Do[A={l,k,j};
%t A276648 B={l+1/2,k+1/2,j+1/2};
%t A276648 If[DecM[A]<=3/4r^2,N1+=1];
%t A276648 If[DecM[B]<=3/4r^2,N2+=1],{l,-r-1,r+1},{k,-r-1,r+1},{j,-r-1,r+1}];
%t A276648 Print[r," ",N1+N2],{r,0,20}]
%Y A276648 Cf. A276450.
%K A276648 nonn
%O A276648 0,2
%A A276648 _Yuriy Sibirmovsky_, Sep 11 2016