A077912 Expansion of 1/(1+x^2-2*x^3).

1, 0, -1, 2, 1, -4, 3, 6, -11, 0, 23, -22, -23, 68, -21, -114, 157, 72, -385, 242, 529, -1012, -45, 2070, -1979, -2160, 6119, -1798, -10439, 14036, 6843, -34914, 21229, 48600, -91057, -6142, 188257, -175972, -200541, 552486, -151403, -953568, 1256375, 650762, -3163511, 1861988, 4465035

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Equally, expansion of (1-x)^(-1)/(1+x+2*x^2).

Links

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

Crossrefs

Cf. A077963.

Programs

GAP

a:=[1,0,-1];; for n in [4..50] do a[n]:=-a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jun 23 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x^2-2*x^3) )); // G. C. Greubel, Jun 23 2019

Mathematica

CoefficientList[Series[1/(1+x^2-2*x^3),{x,0,50}],x] (* or *) LinearRecurrence[{0,-1,2},{1,0,-1},50] (* Harvey P. Dale, Dec 10 2012 *)

PARI

my(x='x+O('x^50)); Vec(1/(1+x^2-2*x^3)) \\ G. C. Greubel, Jun 23 2019

Sage

(1/(1+x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 23 2019

Formula

a(0)=1, a(1)=0, a(2)=-1, a(n) = -a(n-2)+2*a(n-3). - Harvey P. Dale, Dec 10 2012

a(n) = (-1)^n * A077963(n). - G. C. Greubel, Jun 23 2019