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A028966 Norms of vectors in the a.c.c. lattice, divided by 2. 1

%I #13 Sep 08 2022 08:44:50

%S 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,

%T 41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,65,66,68,69,71,72,74,75,

%U 77,78,80,83,84,86,87,89,92,93,95,96,98,99,101,102,104,105,107,108,110,111,113

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

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

%C See A028967 for further information.

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1006/jnth.1994.1073">On lattices equivalent to their duals</a>, J. Number Theory 48 (1994) 373-382.

%e 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 + ...

%p 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

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _James A. Sellers_, May 31 2000

%E Edited by _N. J. A. Sloane_, Sep 29 2006

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)