A078028 Expansion of (1-x)/(1-x^2+2*x^3).

1, -1, 1, -3, 3, -5, 9, -11, 19, -29, 41, -67, 99, -149, 233, -347, 531, -813, 1225, -1875, 2851, -4325, 6601, -10027, 15251, -23229, 35305, -53731, 81763, -124341, 189225, -287867, 437907, -666317, 1013641, -1542131, 2346275, -3569413, 5430537, -8261963, 12569363, -19123037, 29093289

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 (0,1,-2).

Programs

GAP

a:=[1,-1,1];; for n in [4..60] do a[n]:=a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Aug 04 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1-x^2+2*x^3) )); // G. C. Greubel, Aug 04 2019

Maple

seq(coeff(series((1-x)/(1-x^2+2*x^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1-x)/(1-x^2+2*x^3), {x,0,60}], x] (* G. C. Greubel, Aug 04 2019 *)

PARI

Vec((1-x)/(1-x^2+2*x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 25 2012

Sage

((1-x)/(1-x^2+2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019