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A109017
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a(n) = Kronecker symbol (-6/n).
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12
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0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0
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OFFSET
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0,1
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REFERENCES
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L. B. W. Jolley, Summation of Series, Dover Publications, 1961.
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LINKS
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FORMULA
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Euler transform of length-24 sequence [ 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1].
a(n) = -a(-n) = a(n+24) for all n in Z.
G.f.: x * (1 + x^6) / (1 - x^4 + x^8).
G.f.: x *(1 -x^8)*(1 -x^12)^2 /((1 -x^4)*(1 -x^6)*(1 -x^24)).
Sum_{n>=1} |a(n)|/n^2 = Pi^2/9 [Jolley equ. 338].
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EXAMPLE
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G.f. = x + x^5 + x^7 + x^11 - x^13 - x^17 - x^19 - x^23 + x^25 + x^29 + ...
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MAPLE
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numtheory[jacobi](-6, n) ;
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MATHEMATICA
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PROG
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(PARI) {a(n) = kronecker(-6, n)};
(PARI) {a(n) = (n%2) * (n%3!=0) * (-1)^(n\12)};
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CROSSREFS
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KEYWORD
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sign,mult,easy
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AUTHOR
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STATUS
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approved
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