A077953 Expansion of 1/(1-x+2*x^2-2*x^3).

1, 1, -1, -1, 3, 3, -5, -5, 11, 11, -21, -21, 43, 43, -85, -85, 171, 171, -341, -341, 683, 683, -1365, -1365, 2731, 2731, -5461, -5461, 10923, 10923, -21845, -21845, 43691, 43691, -87381, -87381, 174763, 174763, -349525, -349525, 699051, 699051, -1398101, -1398101, 2796203, 2796203, -5592405

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002, Jun 17 2007

Keywords

• sign
• easy

Comments

Essentially the same as A077980.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, -2, 2).

Crossrefs

Cf. A077980.

Cf. A007420, A077925. - Reinhard Zumkeller, Oct 07 2008

Programs

GAP

a:=[1,1,-1];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Aug 07 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+2*x^2-2*x^3) )); // G. C. Greubel, Aug 07 2019

Maple

seq(coeff(series(1/(1-x+2*x^2-2*x^3), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 07 2019

Mathematica

CoefficientList[Series[1/(1-x+2x^2-2x^3),{x,0,50}],x] (* or *) LinearRecurrence[{1,-2,2},{1,1,-1},50] (* Harvey P. Dale, Aug 27 2014 *)

PARI

Vec(1/(1-x+2*x^2-2*x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 25 2012

Sage

(1/(1-x+2*x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 07 2019

Formula

From Reinhard Zumkeller, Oct 07 2008: (Start)

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

a(n) = A077925(floor(n/2)-1) for n>1. (End)