A110308 Expansion of -x*(2+x)/((1+x+x^2)*(1+5*x+x^2)).

0, -2, 11, -52, 247, -1182, 5664, -27140, 130037, -623044, 2985181, -14302860, 68529120, -328342742, 1573184591, -7537580212, 36114716467, -173036002122, 829065294144, -3972290468600, 19032387048857, -91189644775684, 436915836829561, -2093389539372120

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<x>:=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