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A008430
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Theta series of D_8 lattice.
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2
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1, 112, 1136, 3136, 9328, 14112, 31808, 38528, 74864, 84784, 143136, 149184, 261184, 246176, 390784, 395136, 599152, 550368, 859952, 768320, 1175328, 1078784, 1513152, 1362816, 2096192, 1764112, 2496928, 2289280, 3208832, 2731680, 4007808, 3336704
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.
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LINKS
| N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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FORMULA
| G.f.: (theta_3(q^(1/2))^8+theta_4(q^(1/2))^8)/2
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EXAMPLE
| 1 + 112*q^2 + 1136*q^4 + 3136*q^6 + 9328*q^8 + ...
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PROG
| (PARI) {a(n)=if(n<1, n==0, 16*sumdiv(n, d, d^3*(8-d%2)))} /* 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))^8, n))} /* Michael Somos Nov 03 2006 */
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CROSSREFS
| Cf. A008427 (dual), A109773.
A000143(2n)=a(n).
Sequence in context: A203789 A206318 A206311 * A188152 A203915 A188153
Adjacent sequences: A008427 A008428 A008429 * A008431 A008432 A008433
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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