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A244526
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Expansion of f(-x^3, -x^5)^2 in powers of x where f() is Ramanujan's two-variable theta function.
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4
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1, 0, 0, -2, 0, -2, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, -2, 2, -2, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, -2, 0, 0, 3, 0, 2, -2, 0, 0, 2, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, -2, 1, 0, 2, 0, 0, -2, 2, -2, 2, 0, 0, 0, 3, 0, 0
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OFFSET
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0,4
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LINKS
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FORMULA
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Euler transform of period 8 sequence [ 0, 0, -2, 0, -2, 0, 0, -2, ...].
G.f.: f(-x^3, -x^5)^2 = (Sum_{k in Z} (-1)^k * x^(4*k^2 - k))^2.
a(9*n + 4) = a(9*n + 7) = 0. a(49*n + 6) = a(n).
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EXAMPLE
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G.f. = 1 - 2*x^3 - 2*x^5 + x^6 + 2*x^8 + x^10 + 2*x^14 - 2*x^17 + 2*x^18 + ...
G.f. = q - 2*q^25 - 2*q^41 + q^49 + 2*q^65 + q^81 + 2*q^113 - 2*q^137 + ...
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MATHEMATICA
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QP := QPochhammer; A244526[n_]:= SeriesCoefficient[(QP[q^3, q^8]*QP[q^5, q^8]*QP[q^8])^2, {q, 0, n}]; Table[A244526[n], {n, 0, 50}] (* G. C. Greubel, Dec 25 2017 *)
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PROG
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(PARI) {a(n) = (-1)^n * sum(k=0, n, issquare(16*k + 1) * issquare(16*(n-k) + 1))};
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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