login
A222303
Value of t corresponding to norm of n-th shell of points in mcc lattice.
3
0, 1, 2, 0, 4, 2, 5, 4, 1, 8, 9, 10, 8, 0, 5, 10, 2, 13, 4, 9, 16, 17, 18, 1, 16, 8, 13, 20, 18, 10, 5, 20, 17, 0, 25, 26, 9, 16, 2, 26, 18, 4, 29, 13, 20, 25, 32, 8, 34, 17, 32, 29, 10, 1, 36, 34, 26, 37, 36, 5, 40, 16, 41, 25, 40, 32, 37, 18, 9, 0, 34, 20, 45, 29, 2, 36, 41, 13, 4, 49, 50, 40, 45, 26, 17, 52, 50
OFFSET
0,3
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
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
Sequence in context: A361391 A337697 A328599 * A097945 A319997 A153733
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 14 2013
EXTENSIONS
a(18) onwards computed by Warren D. Smith
STATUS
approved