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A222302 Value of s corresponding to norm of n-th shell of points in mcc lattice. 3
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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).

The norms q = X.X of the lattice points X have the form q = s/2 + t/sqrt(2) for integers s and t.

A222301 gives the number of points with each successive value of q; A222302 and A222303 give the corresponding values of s and t.

REFERENCES

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].)

LINKS

Table of n, a(n) for n=0..91.

J. H. Conway and N. J. A. Sloane, On lattices equivalent to their duals, J. Number Theory 48 (1994) 373-382.

J. H. Conway and N. J. A. Sloane, The Optimal Isodual Lattice Quantizer in Three Dimensions, Advances in Math. of Commun., Vol. 1, No. 2 (2007), 257-260; arXiv:math/0701080 [math.NT], 2007.

G. Nebe and N. J. A. Sloane, Home page for mcc lattice.

Warren D. Smith, The theta series of the (det=1, isodual) MCC lattice. [Gives first 775 terms.]

CROSSREFS

Cf. A222301, A222303.

Sequence in context: A226787 A140574 A010636 * A222617 A204695 A175435

Adjacent sequences:  A222299 A222300 A222301 * A222303 A222304 A222305

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 14 2013

EXTENSIONS

a(18) onwards computed by Warren D. Smith.

STATUS

approved

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)