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A276648
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Number of points of norm <= n in the body-centered cubic lattice with the lattice parameter equal to 2/sqrt(3).
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1
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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