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A110309
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Expansion of (1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)).
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5
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1, -3, 12, -57, 275, -1320, 6325, -30303, 145188, -695637, 3332999, -15969360, 76513801, -366599643, 1756484412, -8415822417, 40322627675, -193197315960, 925663952125, -4435122444663, 21249948271188, -101814618911277, 487823146285199, -2337301112514720
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n+2) = - 5*a(n+1) - a(n) + (-1)^n*A109265(n+3).
a(n) = -6*a(n-1) - 7*a(n-2) - 6*a(n-3) - a(n-4) for n>3. - Colin Barker, Apr 30 2019
a(n) = (1/2)*(ChebyshevU(n, -5/2) + ChebyshevU(n, -1/2)). - G. C. Greubel, Jan 03 2023
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MAPLE
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seriestolist(series((1+3*x+x^2)/((x^2+5*x+1)*(x^2+x+1)), x=0, 25));
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MATHEMATICA
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LinearRecurrence[{-6, -7, -6, -1}, {1, -3, 12, -57}, 40] (* G. C. Greubel, Jan 03 2023 *)
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PROG
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(PARI) Vec((1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25)) \\ Colin Barker, Apr 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) )); // G. C. Greubel, Jan 03 2023
(SageMath)
def A110309(n): return (1/2)*(chebyshev_U(n, -5/2)+chebyshev_U(n, -1/2))
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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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