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

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

Author

Yuriy Sibirmovsky, Sep 11 2016

Keywords

• nonn

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.

Examples

			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.
		

Links

• Yuriy Sibirmovsky, Table of n, a(n) for n = 0..50
• N. G. Khlebtsov, T-matrix method in plasmonics: An overview, J. Quantitative Spectroscopy & Radiative Transfer 123 (2013) 184-217.

Crossrefs

Cf. A276450.

Programs

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}]