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A008424
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Theta series of {D_9}* lattice.
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2
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1, 0, 0, 0, 18, 0, 0, 0, 144, 512, 0, 0, 672, 0, 0, 0, 2034, 4608, 0, 0, 4320, 0, 0, 0, 7392, 18432, 0, 0, 12672, 0, 0, 0, 22608, 47616, 0, 0, 34802, 0, 0, 0, 44640, 101376, 0, 0, 60768, 0, 0, 0, 93984, 193536, 0, 0, 125280, 0, 0, 0, 141120, 324096, 0, 0
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OFFSET
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0,5
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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. 120.
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LINKS
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FORMULA
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Theta series in terms of Jacobi theta series: (theta_2)^9 + (theta_3)^9. - Sean A. Irvine, Mar 28 2018
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EXAMPLE
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G.f. = 1 + 18*q^4 + 144*q^8 + ...
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PROG
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(PARI)
N=66; q='q+O('q^N);
T3(q) = eta(q^2)^5 / ( eta(q)^2 * eta(q^4)^2 );
T2(q) = eta(q^4)^2 / eta(q^2);
Vec( T3(q^4)^9 + (2 * q * T2(q^4))^9 )
(Magma)
L := Dual(Lattice("D", 9));
B := Basis(ThetaSeriesModularFormSpace(L), 100);
S := [ 1, 0, 0, 0, 18];
Coefficients(&+[B[i] * S[i] : i in [1..5]]); // Andy Huchala, Jul 24 2021
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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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EXTENSIONS
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STATUS
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approved
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