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

Author

Paul Barry, Nov 18 2009

Keywords

• easy
• sign

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).

Crossrefs

Cf. A168053.

Programs

Mathematica

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

PARI

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

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)

Extensions

Corrected by R. J. Mathar, Dec 03 2014