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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 31 2000
Edited by N. J. A. Sloane, Sep 29 2006
STATUS
approved