%I M2347 #43 Nov 07 2022 07:41:40
%S 0,3,4,8,11,12,16,19,20,24,27,32,35,36,40,43,44,48,51,52,56,59,64,67,
%T 68,72,75,76,80,83,84,88,91,96,99,100,104,107,108,115,116,120,123,128,
%U 131,132,136,139,140,144,147,148,152,155,160,163,164,168
%N Norms of vectors in the b.c.c. lattice.
%C Integers such that A004013(n) is nonzero. - _Michael Somos_, Jul 28 2014
%C A subsequence of A047458. The complement seems to be 4*A004215. - _Andrey Zabolotskiy_, Nov 11 2021
%C From _Mohammed Yaseen_, Nov 06 2022: (Start)
%C These are numbers of the form x^2+y^2+z^2 where x, y and z are either all even (including zero) or all odd.
%C The selection rule for the planes with Miller indices (hkl) to undergo X-ray diffraction in an f.c.c. lattice is h^2+k^2+l^2 = N where N is a term of this sequence. See A000378 for simple cubic lattice. (End)
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116. (Chapter 4 section 6.7)
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Robert Israel, <a href="/A004014/b004014.txt">Table of n, a(n) for n = 0..10000</a>
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds3.html">Home page for this lattice</a>
%H <a href="/index/Ba#bcc">Index entries for sequences related to b.c.c. lattice</a>
%p f:= JacobiTheta2(0,z^4)^3+JacobiTheta3(0,z^4)^3:
%p S:= series(f,z,1001):
%p select(t -> coeff(S,z,t) <> 0, [$0..1000]); # _Robert Israel_, Oct 18 2015
%t f = EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3; S = f + O[z]^200; Flatten[Position[CoefficientList[S, z], _?Positive] - 1] (* _Jean-François Alcover_, Oct 23 2016, after _Robert Israel_ *)
%Y Cf. A004013, A047458, A004215.
%Y Union of A034045 and A017101. - _Mohammed Yaseen_, Nov 06 2022
%K nonn,nice,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Oct 17 2015