A078025 Expansion of (1-x)/(1-2*x^2+2*x^3).

1, -1, 2, -4, 6, -12, 20, -36, 64, -112, 200, -352, 624, -1104, 1952, -3456, 6112, -10816, 19136, -33856, 59904, -105984, 187520, -331776, 587008, -1038592, 1837568, -3251200, 5752320, -10177536, 18007040, -31859712, 56369152, -99733504, 176457728, -312205312, 552382464

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 (0,2,-2)

Programs

GAP

a:=[1,-1,2];; for n in [4..40] do a[n]:=2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Aug 04 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-2*x^2+2*x^3) )); // G. C. Greubel, Aug 04 2019

Maple

seq(coeff(series((1-x)/(2*x^3-2*x^2+1), x, n+1), x, n), n = 0..40); # G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1-x)/(1-2*x^2+2*x^3), {x,0,40}], x] (* G. C. Greubel, Aug 04 2019 *)

PARI

Vec((1-x)/(1-2*x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

((1-x)/(1-2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019