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Search: id:A008428
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| A008428 |
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Theta series of D_6 lattice. |
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+0
1
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| 1, 60, 252, 544, 1020, 1560, 2080, 3264, 4092, 4380, 6552, 8160, 8224, 10200, 12480, 14144, 16380, 17400, 18396, 24480, 26520, 23040, 31200, 35904, 32800, 39060, 42840, 44608, 49344, 50520, 54080, 65280, 65532, 57600, 73080, 84864, 74460
(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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LINKS
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G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
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G.f.: (theta_3(q^(1/2))^6+theta_4(q^(1/2))^6)/2
Expansion of ( phi(q)^6 + phi(-q)^6 ) / 2 in powers of q^2 where phi() is a Ramanujan theta function. - Michael Somos Sep 14 2007
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EXAMPLE
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1 + 60*q^2 + 252*q^4 + 544*q^6 + 1020*q^8 + ...
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, 4*sumdiv(n, d, d^2* (16*kronecker(-4, n/d)-kronecker(-4, d))))} /* Michael Somos Nov 03 2006 */
(PARI) {a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^6, n))} /* Michael Somos Nov 03 2006 */
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CROSSREFS
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A000141(2n)=a(n).
Adjacent sequences: A008425 A008426 A008427 this_sequence A008429 A008430 A008431
Sequence in context: A103741 A140873 A019285 this_sequence A075295 A134587 A100153
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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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