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A164117
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Expansion of (1 - x) * (1 - x^10) / ((1 - x^2) * (1 - x^4) * (1 - x^5)) in powers of x.
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3
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1, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2, -1, 1, -1, 2
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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Euler transform of length 10 sequence [-1, 1, 0, 1, 1, 0, 0, 0, 0, -1].
a(n) = -b(n) where b(n) is multiplicative with b(2) = -1, b(2^e) = -2 if e>1, b(p^e) = 1 if p>2.
a(n) = a(-n) for all n in Z. a(n+4) = a(n) unless n=0 or n=-4.
G.f.: (1 - x + x^2 - x^3 + x^4) / (1 - x^4).
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EXAMPLE
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G.f. = 1 - x + x^2 - x^3 + 2*x^4 - x^5 + x^6 - x^7 + 2*x^8 - x^9 + x^10 + ...
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MATHEMATICA
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CoefficientList[Series[(1-x)(1-x^10)/((1-x^2)(1-x^4)(1-x^5)), {x, 0, 120}], x] (* Harvey P. Dale, Nov 28 2014 *)
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PROG
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(PARI) {a(n) = (-1)^n - (n==0) + (n%4==0)};
(PARI) {a(n) = -(n==0) + [2, -1, 1, -1][n%4 + 1]};
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1-x^10)/((1-x^2)*(1-x^4)*(1-x^5)))); // G. C. Greubel, Sep 25 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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