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Search: id:A008429
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| A008429 |
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Theta series of D_7 lattice. |
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+0
1
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| 1, 84, 574, 1288, 3444, 4424, 9240, 11088, 18494, 19740, 34440, 31304, 52808, 52248, 74048, 71120, 110964, 94864, 145222, 132888, 181384, 163856, 249480, 201040, 295960, 264684, 346696, 314272, 454608, 352520, 518336, 452256, 591934, 517216
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.
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FORMULA
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G.f.: (theta_3(q^(1/2))^7+theta_4(q^(1/2))^7)/2
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EXAMPLE
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1 + 84*q^2 + 574*q^4 + 1288*q^6 + 3444*q^8 + ...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^7, n))} /* Michael Somos Nov 03 2006 */
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CROSSREFS
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A008451(2n)=a(n).
Sequence in context: A131072 A083986 A064198 this_sequence A069080 A093284 A027794
Adjacent sequences: A008426 A008427 A008428 this_sequence A008430 A008431 A008432
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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