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A112690
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Expansion of 1/(1 + x^2 - x^3 - x^5).
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1
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0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/((1+x^2)*(1-x^3)).
a(n) = Sum_{k=0..n} Sum_{j=0..floor((k+1)/2)} (-1)^(k-j)*C(k-j+1, j-1).
E.g.f.: (3*sin(x) + 3*cos(x) + exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/6.
a(n) = (3*sin(Pi*n/2) + 3*cos(Pi*n/2) - 4*cos(2*Pi*n/3) + 1)/6. (End)
a(n) = 2*floor(n/4) + floor((n+2)/3) - floor(n/3) - floor(n/2). - Ridouane Oudra, Mar 11 2023
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MATHEMATICA
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LinearRecurrence[{0, -1, 1, 0, 1}, {0, 1, 0, -1, 1}, 100] (* Vincenzo Librandi, Jul 07 2016 *)
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PROG
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(PARI) concat(0, Vec(1/(1+x^2-x^3-x^5) + O(x^80))) \\ Michel Marcus, Jul 07 2016
(PARI) a(n) = round(real((exp(-2/3*I*n*Pi)*(-4+(3+3*I)*exp((I*n*Pi)/6) + 2*exp((2*I*n*Pi)/3) + (3-3*I)*exp((7*I*n*Pi)/6) - 4*exp((4*I*n*Pi)/3)))/12)) \\ Colin Barker, Jul 07 2016
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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