A168071 Expansion of (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)).

1, 1, -2, -5, -5, -8, -11, -11, -14, -17, -17, -20, -23, -23, -26, -29, -29, -32, -35, -35, -38, -41, -41, -44, -47, -47, -50, -53, -53, -56, -59, -59, -62, -65, -65, -68, -71, -71, -74, -77, -77, -80, -83, -83, -86, -89, -89, -92, -95, -95, -98, -101, -101, -104, -107, -107, -110, -113, -113

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

G.f.: (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)).

a(n) = A168072(n)/3^n.

From Wesley Ivan Hurt, Oct 05 2017: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3.

a(n) = (45 - 48*n + 18*cos(2*(n-1)*Pi/3) - 9*cos(Pi*cos(2*(n-1)*Pi/3) + Pi*sin(2*(n-1)*Pi/3)/sqrt(3)) + 14*sqrt(3)*sin(2*(n-1)*Pi/3))/24. (End)

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {1, 1, -2, -5}, 50] (* G. C. Greubel, Jul 08 2016 *)

Prog

(PARI) Vec((1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)) + O(x^70)) \\ Michel Marcus, Dec 03 2014

Crossrefs

Cf. A168053.

Sequence in context: A251736 A076520 A014249 * A361861 A330447 A145420

Adjacent sequences: A168068 A168069 A168070 * A168072 A168073 A168074

Keyword

easy,sign

Author

Paul Barry, Nov 18 2009

Extensions

Corrected by R. J. Mathar, Dec 03 2014

Status

approved