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Search: id:A028966
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| A028966 |
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Norms of vectors in the a.c.c. lattice, divided by 2. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, On Lattices Equivalent to Their Duals, J. Number Theory, 48 (1994), 373-382.
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EXAMPLE
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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 + ...
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MAPLE
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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: (Sellers)
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PROGRAM
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(MAGMA) L:=LatticeWithGram(3, [4, -1, -1, -1, 4, -2, -1, -2, 4]); T<q> := ThetaSeries(L, 500); T;
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CROSSREFS
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Adjacent sequences: A028963 A028964 A028965 this_sequence A028967 A028968 A028969
Sequence in context: A028731 A028740 A028794 this_sequence A028767 A138529 A035057
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 31 2000
Edited by njas, Sep 29 2006
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