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A028967 Theta series of a.c.c. lattice. 4
1, 0, 10, 4, 0, 8, 12, 0, 26, 0, 0, 8, 20, 0, 32, 8, 0, 16, 10, 0, 40, 8, 0, 16, 28, 0, 40, 4, 0, 8, 32, 0, 58, 16, 0, 16, 0, 0, 72, 8, 0, 16, 40, 0, 40, 8, 0, 32, 52, 0, 50, 8, 0, 24, 12, 0, 64, 16, 0, 24, 40, 0, 96, 0, 0, 16, 40, 0, 80, 16, 0, 16, 26, 0, 40, 20, 0, 32, 64, 0, 104, 0, 0, 40, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

At one time Conway and I called this the z.c.c. lattice, which has led to some confusion. The a.c.c. and z.c.c. are different names for the same lattice. The a.c.c. name is preferred.

Gram matrix:

[ +4 -1 +1]

[ -1 +4 +2]

[ +1 +2 +4]

This lattice has determinant 36 and kissing number 10; it is not isodual.

LINKS

John Cannon, Table of n, a(n) for n = 0..5000

J. H. Conway and N. J. A. Sloane, On Lattices Equivalent to Their Duals, J. Number Theory, 48 (1994), 373-382.

K. L. Fields, The fragile lattice packings of spheres in three-dimensional space, Acta Cryst. Sect. A 36 (1980), 194-197.

A. Patterson, Crystal lattice models based on the close packing of spheres, Rev. Sci. Instrumen., 12 (1941), 206-211.

EXAMPLE

1 + 10*q^4 + 4*q^6 + 8*q^10 + 12*q^12 + 26*q^16 + 8*q^22 + 20*q^24 + 32*q^28 + 8*q^30 + ...

PROG

(MAGMA) L:=LatticeWithGram(3, [4, -1, -1, -1, 4, -2, -1, -2, 4]); T<q> := ThetaSeries(L, 500); T;

CROSSREFS

Cf. A028966.

Sequence in context: A077194 A038305 A089478 * A097530 A063565 A177390

Adjacent sequences:  A028964 A028965 A028966 * A028968 A028969 A028970

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by N. J. A. Sloane, Sep 29 2006

STATUS

approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)