A077970 Expansion of 1/(1+x-2*x^2+2*x^3).

1, -1, 3, -7, 15, -35, 79, -179, 407, -923, 2095, -4755, 10791, -24491, 55583, -126147, 286295, -649755, 1474639, -3346739, 7595527, -17238283, 39122815, -88790435, 201512631, -457339131, 1037945263, -2355648787, 5346217575, -12133405675, 27537138399, -62496384899, 141837473047

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 (-1, 2, -2).

Crossrefs

Cf. A077946, A078040.

Programs

GAP

a:=[1,1,-3];; for n in [4..40] do a[n]:=-a[n-1]+2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 24 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+x-2*x^2+2*x^3) )); // G. C. Greubel, Jun 24 2019

Mathematica

CoefficientList[Series[1/(1+x-2x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-1,2,-2},{1,-1,3},40] (* Harvey P. Dale, Sep 29 2018 *)

PARI

Vec(1/(1+x-2*x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1+x-2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019

Formula

a(n) = (-1)^n*A077946(n). - R. J. Mathar, Feb 28 2019