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A192323
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Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.
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1
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1, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 6, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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Euler transform of period 60 sequence.
G.f.: (Sum_{k} x^(3 * k^2)) * (Sum_{k} x^(5 * k^2)).
a(3*n + 1) = a(4*n + 2) = a(5*n + 1) = a(5*n + 4) = 0. a(4*n) = A028956(n).
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EXAMPLE
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1 + 2*q^3 + 2*q^5 + 4*q^8 + 2*q^12 + 4*q^17 + 2*q^20 + 4*q^23 + 2*q^27 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] EllipticTheta[ 3, 0, q^5], {q, 0, n}]
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PROG
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(PARI) {a(n) = if( n<1, n==0, qfrep([3, 0; 0, 5], n)[n]*2)}
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A))^5 / (eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A))^2, n))}
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CROSSREFS
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Cf. A028956.
Sequence in context: A193511 A058087 A073274 * A071957 A002655 A064891
Adjacent sequences: A192320 A192321 A192322 * A192324 A192325 A192326
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 01 2011
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STATUS
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approved
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