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%I A222302 #14 Dec 05 2018 17:25:46
%S A222302 0,1,0,4,0,4,1,4,9,0,1,0,4,16,9,4,16,1,16,9,0,1,0,25,4,16,9,0,4,16,25,
%T A222302 4,9,36,1,0,25,16,36,4,16,36,1,25,16,9,0,36,0,25,4,9,36,49,0,4,16,1,4,
%U A222302 49,0,36,1,25,4,16,9,36,49,64,16,36,1,25,64,16,9,49,64,1,0,16,9,36,49,0,4,64,1,25,4,64
%N A222302 Value of s corresponding to norm of n-th shell of points in mcc lattice.
%C A222302 The mcc lattice is generated by the vectors (u,v,0), (u,0,v) and (0,v,v), where u = 2^(-1/2), v = 2^(-1/4).
%C A222302 The norms q = X.X of the lattice points X have the form q = s/2 + t/sqrt(2) for integers s and t.
%C A222302 A222301 gives the number of points with each successive value of q; A222302 and A222303 give the corresponding values of s and t.
%D A222302 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. p. xxiv. (Note that the second set of generators should be [0, +-v, +-v].)
%H A222302 J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1006/jnth.1994.1073">On lattices equivalent to their duals</a>, J. Number Theory 48 (1994) 373-382.
%H A222302 J. H. Conway and N. J. A. Sloane, <a href="http://arxiv.org/abs/math/0701080">The Optimal Isodual Lattice Quantizer in Three Dimensions</a>, Advances in Math. of Commun., Vol. 1, No. 2 (2007), 257-260; arXiv:math/0701080 [math.NT], 2007.
%H A222302 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/mcc.html">Home page for mcc lattice</a>.
%H A222302 Warren D. Smith, <a href="/A222301/a222301.txt">The theta series of the (det=1, isodual) MCC lattice</a>. [Gives first 775 terms.]
%Y A222302 Cf. A222301, A222303.
%K A222302 nonn
%O A222302 0,4
%A A222302 _N. J. A. Sloane_, Feb 14 2013
%E A222302 a(18) onwards computed by _Warren D. Smith_.

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