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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 := 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 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.)