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
Keywords
Examples
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 + ...
Links
- J. H. Conway and N. J. A. Sloane, On lattices equivalent to their duals, J. Number Theory 48 (1994) 373-382.
Programs
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Magma
L:=LatticeWithGram(3, [4,-1,-1, -1,4,-2, -1,-2,4]); T
:= ThetaSeries(L,500); T;
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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 Sellers, May 31 2000
Extensions
More terms from James Sellers, May 31 2000
Edited by N. J. A. Sloane, Sep 29 2006
Comments