A077984 Expansion of 1/(1+2*x-2*x^2+2*x^3).

1, -2, 6, -18, 52, -152, 444, -1296, 3784, -11048, 32256, -94176, 274960, -802784, 2343840, -6843168, 19979584, -58333184, 170311872, -497249280, 1451788672, -4238699648, 12375475200, -36131927040, 105492203776, -307999212032, 899246685696, -2625476203008, 7665444201472

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2, 2, -2).

Crossrefs

Cf. A077835.

Programs

GAP

a:=[1,-2,6];; for n in [4..30] do a[n]:=-2*a[n-1]+2*a[n-2] - 2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1+2*x-2*x^2+2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

CoefficientList[Series[1/(1+2x-2x^2+2x^3),{x,0,30}],x] (* or *) LinearRecurrence[{-2,2,-2},{1,-2,6},30] (* Harvey P. Dale, Jun 17 2014 *)

PARI

my(x='x+O('x^30)); Vec(1/(1+2*x-2*x^2+2*x^3)) \\ G. C. Greubel, Jun 25 2019

Sage

(1/(1+2*x-2*x^2+2*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(n) = -2*a(n-1) + 2*a(n-2) - 2*a(n-3).

a(n) is the nearest integer to c*d^n where c=0.7166689603... satisfies 67*c^3 - 67*c^2 + 15*c - 1 = 0 and d=-2.9196395658... satisfies d^3 + 2*d^2 - 2*d + 2 = 0.

a(n) = (-1)^n * A077835(n). - R. J. Mathar, Aug 07 2015