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

%I A028966 #16 Jul 08 2025 18:59:08
%S A028966 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 A028966 41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,65,66,68,69,71,72,74,75,
%U A028966 77,78,80,83,84,86,87,89,92,93,95,96,98,99,101,102,104,105,107,108,110,111,113
%N A028966 Norms of vectors in the a.c.c. lattice, divided by 2.
%C A028966 Equivalently, numbers represented by quadratic form with Gram matrix [ 4, 2, 1; 2, 4, 2; 1, 2, 4 ], divided by 2.
%C A028966 See A028967 for further information.
%H A028966 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 A028966 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 A028966 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
%o A028966 (Magma) L:=LatticeWithGram(3, [4,-1,-1, -1,4,-2, -1,-2,4]); T<q> := ThetaSeries(L,500); T;
%K A028966 nonn
%O A028966 0,2
%A A028966 _N. J. A. Sloane_
%E A028966 More terms from _James Sellers_, May 31 2000
%E A028966 Edited by _N. J. A. Sloane_, Sep 29 2006