This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004014 M2347 #43 Nov 07 2022 07:41:40 %S A004014 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 A004014 68,72,75,76,80,83,84,88,91,96,99,100,104,107,108,115,116,120,123,128, %U A004014 131,132,136,139,140,144,147,148,152,155,160,163,164,168 %N A004014 Norms of vectors in the b.c.c. lattice. %C A004014 Integers such that A004013(n) is nonzero. - _Michael Somos_, Jul 28 2014 %C A004014 A subsequence of A047458. The complement seems to be 4*A004215. - _Andrey Zabolotskiy_, Nov 11 2021 %C A004014 From _Mohammed Yaseen_, Nov 06 2022: (Start) %C A004014 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 A004014 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 A004014 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116. (Chapter 4 section 6.7) %D A004014 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A004014 Robert Israel, <a href="/A004014/b004014.txt">Table of n, a(n) for n = 0..10000</a> %H A004014 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 A004014 <a href="/index/Ba#bcc">Index entries for sequences related to b.c.c. lattice</a> %p A004014 f:= JacobiTheta2(0,z^4)^3+JacobiTheta3(0,z^4)^3: %p A004014 S:= series(f,z,1001): %p A004014 select(t -> coeff(S,z,t) <> 0, [$0..1000]); # _Robert Israel_, Oct 18 2015 %t A004014 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 A004014 Cf. A004013, A047458, A004215. %Y A004014 Union of A034045 and A017101. - _Mohammed Yaseen_, Nov 06 2022 %K A004014 nonn,nice,easy %O A004014 0,2 %A A004014 _N. J. A. Sloane_ %E A004014 More terms from _Sean A. Irvine_, Oct 17 2015