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A180318
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Expansion of a(-q) in powers of q where a(q) is a cubic AGM function.
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0
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1, -6, 0, -6, 6, 0, 0, -12, 0, -6, 0, 0, 6, -12, 0, 0, 6, 0, 0, -12, 0, -12, 0, 0, 0, -6, 0, -6, 12, 0, 0, -12, 0, 0, 0, 0, 6, -12, 0, -12, 0, 0, 0, -12, 0, 0, 0, 0, 6, -18, 0, 0, 12, 0, 0, 0, 0, -12, 0, 0, 0, -12, 0, -12, 6, 0, 0, -12, 0, 0, 0, 0, 0, -12, 0, -6, 12, 0, 0, -12, 0, -6, 0, 0, 12, 0, 0, 0, 0, 0, 0, -24, 0, -12
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..93.
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FORMULA
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Expansion of 2 * a(q^4) - a(q) in powers of q.
Expansion of theta_3(-q) * theta_3(-q^3) - theta_2(q) * theta_2(q^3) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = - (12)^(1/2) (t/i) f(t) where q = exp(2 pi i t).
a(n) = (-1)^n * A004016(n).
G.f.: 1 + 6 * Sum_{k>0} (-x)^k/(1 + (-x)^k + x^(2*k)) = Sum_{j,k} (-x)^(j*j + j*k + k*k).
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EXAMPLE
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1 - 6*q - 6*q^3 + 6*q^4 - 12*q^7 - 6*q^9 + 6*q^12 - 12*q^13 + 6*q^16 + ...
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PROG
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(PARI) {a(n) = if( n<1, n==0, 6 * (-1)^n * sumdiv(n, d, kronecker(d, 3)))}
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CROSSREFS
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Sequence in context: A198499 A092605 A004016 * A093577 A065442 A198752
Adjacent sequences: A180315 A180316 A180317 * A180319 A180320 A180321
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 27 2010
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STATUS
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approved
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