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 A110308 Expansion of -x*(2+x)/((1+x+x^2)*(1+5*x+x^2)). 5
 0, -2, 11, -52, 247, -1182, 5664, -27140, 130037, -623044, 2985181, -14302860, 68529120, -328342742, 1573184591, -7537580212, 36114716467, -173036002122, 829065294144, -3972290468600, 19032387048857, -91189644775684, 436915836829561, -2093389539372120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-6,-7,-6,-1). FORMULA a(n+2) = - 5*a(n+1) - a(n) - A099837(n+2). 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)*(2*U(n, -5/2) + U(n-1, -5/2) - 2*U(n, -1/2) - U(n-1, -1/2)), where U(n, x) = ChebyshevU(n, x). - G. C. Greubel, Jan 03 2023 MAPLE seriestolist(series(-x*(2+x)/((x^2+x+1)*(x^2+5*x+1)), x=0, 25)); MATHEMATICA LinearRecurrence[{-6, -7, -6, -1}, {0, -2, 11, -52}, 40] (* G. C. Greubel, Jan 03 2023 *) PROG (PARI) concat(0, Vec(-x*(2+x)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25))) \\ Colin Barker, Apr 30 2019 (Magma) R:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( -x*(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 A110308(n): return (1/4)*(2*U(n, -5/2) +U(n-1, -5/2) -2*U(n, -1/2) -U(n-1, -1/2)) [A110308(n) for n in range(41)] # G. C. Greubel, Jan 03 2023 CROSSREFS Cf. A004253, A049347, A099837, A110307, A110309, A110310, A110311. Sequence in context: A026986 A181290 A026996 * A027201 A026933 A346925 Adjacent sequences: A110305 A110306 A110307 * A110309 A110310 A110311 KEYWORD easy,sign AUTHOR Creighton Dement, Jul 19 2005 STATUS approved

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)