A028966 Norms of vectors in the a.c.c. lattice, divided by 2.

0, 2, 3, 5, 6, 8, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 83, 84, 86, 87, 89, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105, 107, 108, 110, 111, 113

Offset

0,2

Comments

Equivalently, numbers represented by quadratic form with Gram matrix [ 4, 2, 1; 2, 4, 2; 1, 2, 4 ], divided by 2.

See A028967 for further information.

Links

Table of n, a(n) for n=0..70.

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

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 + ...

Maple

L := [seq(0, i=1..1)]: for x from -20 to 20 do for y from -20 to 20 do for z from -20 to 20 do if member(4*x^2+4*x*y+2*x*z+4*y^2+4*y*z+4*z^2, L)=false then L := [op(L), 4*x^2 +4*x*y+2*x*z+4*y^2+4*y*z+4*z^2] fi: od: od: od: L2 := sort(L): for i from 1 to 100 do printf(`%d, `, L2[i]/2) od: # James A. Sellers, May 31 2000

Prog

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

Crossrefs

Sequence in context: A028731 A028740 A028794 * A028767 A268226 A138529

Adjacent sequences: A028963 A028964 A028965 * A028967 A028968 A028969

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from James A. Sellers, May 31 2000

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

Status

approved