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A246863
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Expansion of phi(x) * f(x^1, x^7) in powers of x where phi(), f() are Ramanujan theta functions.
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2
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1, 3, 2, 0, 2, 2, 0, 1, 2, 2, 3, 4, 0, 0, 2, 0, 4, 2, 0, 2, 0, 0, 1, 4, 0, 2, 6, 1, 2, 0, 0, 4, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 4, 0, 1, 4, 2, 0, 4, 2, 0, 3, 2, 2, 0, 4, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 3, 4, 0, 0, 2, 4, 2, 0, 0, 3, 4
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Euler transform of period 16 sequence [ 3, -4, 2, -1, 2, -3, 3, -2, 3, -3, 2, -1, 2, -4, 3, -2, ...].
a(9*n + 3) = a(9*n + 6) = 0. a(9*n) = A246862(n).
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EXAMPLE
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G.f. = 1 + 3*x + 2*x^2 + 2*x^4 + 2*x^5 + x^7 + 2*x^8 + 2*x^9 + 3*x^10 + ...
G.f. = q^9 + 3*q^25 + 2*q^41 + 2*q^73 + 2*q^89 + q^121 + 2*q^137 + 2*q^153 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x] QPochhammer[ -x^1, x^8] QPochhammer[ -x^7, x^8] QPochhammer[ x^8], {x, 0, n}];
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PROG
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(PARI) {a(n) = if( n<0, 0, issquare(16 * n + 9) + 2 * sum(i=1, sqrtint(n), issquare(16 * (n - i^2) + 9)))};
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CROSSREFS
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Cf. A000122, A008441, A113407, A116604, A125079, A129447, A134343, A138741,A214263, A226192, A246862.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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