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A230205
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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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1
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1, -1, -2, 0, 2, 2, 0, 1, -2, -2, -1, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 1, 0, 0, -2, 2, 1, -2, 0, 0, 0, -2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 1, 0, -2, 0, 0, -2, 0, -1, -2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, -1, -4, 0, 0
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OFFSET
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0,3
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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 [ -1, -2, -2, -1, -2, -1, -1, -2, -1, -1, -2, -1, -2, -2, -1, -2, ...].
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EXAMPLE
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G.f. = 1 - x - 2*x^2 + 2*x^4 + 2*x^5 + x^7 - 2*x^8 - 2*x^9 - x^10 + ...
G.f. = q^9 - 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[4, 0, q]*QPochhammer[-q^1, q^8]* QPochhammer[-q^7, q^8]*QPochhammer[q^8], {q, 0, n}];
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PROG
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(PARI) {a(n) = local(m, j); if( n<0, 0, m = 16*n + 9; sum( k=0, sqrtint(m \ 4), if( issquare(m - 16*k^2, &j), if( k==0, 1, 2) * (-1)^k * ((j%8)==3 || (j%8==5)))))}
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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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