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A008430
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Theta series of D_8 lattice.
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5
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (theta_3(q^(1/2))^8 + theta_4(q^(1/2))^8)/2.
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EXAMPLE
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1 + 112*q^2 + 1136*q^4 + 3136*q^6 + 9328*q^8 + ...
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MATHEMATICA
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a[n_] := 16*DivisorSum[n, #^3*(8 - Mod[#, 2]) &]; a[0] = 1; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 02 2015, adapted from PARI *)
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PROG
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(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
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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