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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 (list; graph; refs; listen; history; text; internal format)
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

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.

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

Adjacent sequences:  A276645 A276646 A276647 * A276649 A276650 A276651

KEYWORD

nonn

AUTHOR

Yuriy Sibirmovsky, Sep 11 2016

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)