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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
1, 9, 59, 169, 339, 701, 1243, 1893, 2741, 3943, 5577, 7343, 9409, 12039, 15065, 18421, 22227, 26717, 31879, 37461, 43655, 50557, 58071, 66227, 75121, 85083, 95801, 107227, 119541, 133019, 147271, 161901, 178127, 195481, 214143
OFFSET
0,2
COMMENTS
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.
First 5 terms are the same as A276450.
LINKS
N. G. Khlebtsov, T-matrix method in plasmonics: An overview, J. Quantitative Spectroscopy & Radiative Transfer 123 (2013) 184-217.
EXAMPLE
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.
MATHEMATICA
DecM[A_]:=A[[1]]^2+A[[2]]^2+A[[3]]^2;
Do[N1=0; N2=0;
Do[A={l, k, j};
B={l+1/2, k+1/2, j+1/2};
If[DecM[A]<=3/4r^2, N1+=1];
If[DecM[B]<=3/4r^2, N2+=1], {l, -r-1, r+1}, {k, -r-1, r+1}, {j, -r-1, r+1}];
Print[r, " ", N1+N2], {r, 0, 20}]
CROSSREFS
Cf. A276450.
Sequence in context: A196211 A196679 A276450 * A308353 A280103 A174654
KEYWORD
nonn
AUTHOR
Yuriy Sibirmovsky, Sep 11 2016
STATUS
approved