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A110307
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Expansion of (1+2*x)/((1+x+x^2)*(1+5*x+x^2)).
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5
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1, -4, 17, -80, 384, -1842, 8827, -42292, 202631, -970862, 4651680, -22287540, 106786021, -511642564, 2451426797, -11745491420, 56276030304, -269634660102, 1291897270207, -6189851690932, 29657361184451, -142096954231322, 680827409972160, -3262040095629480
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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) - A099837(n+1).
a(n) + a(n+1) + a(n+2) = A002320(n).
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) = (1/4)*(3*U(n,-5/2) + U(n-1,-5/2) + U(n,-1/2) - U(n-1,-1/2)), where U(n, x) = ChebyshevU(n, x). - G. C. Greubel, Jan 03 2023
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MAPLE
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seriestolist(series((1+2*x)/((x^2+x+1)*(x^2+5*x+1)), x=0, 25));
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MATHEMATICA
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LinearRecurrence[{-6, -7, -6, -1}, {1, -4, 17, -80}, 41] (* G. C. Greubel, Jan 03 2023 *)
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PROG
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(PARI) Vec((1+2*x)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25)) \\ Colin Barker, Apr 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+2*x)/((1+x+x^2)*(1+5*x+x^2)) )); // G. C. Greubel, Jan 03 2023
(SageMath)
def U(n, x): return chebyshev_U(n, x)
def A110307(n): return (1/4)*(3*U(n, -5/2) +U(n-1, -5/2) +U(n, -1/2) -U(n-1, -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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