A222302 Value of s corresponding to norm of n-th shell of points in mcc lattice.

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

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