A078011 Expansion of (1-x)/(1-x-x^2+2*x^3).

1, 0, 1, -1, 0, -3, -1, -4, 1, -1, 8, 5, 15, 4, 9, -17, -16, -51, -33, -52, 17, 31, 152, 149, 239, 84, 25, -369, -512, -931, -705, -612, 545, 1343, 3112, 3365, 3791, 932, -2007, -8657, -12528, -17171, -12385, -4500, 17457, 37727, 64184, 66997, 55727, -5644, -83911, -201009, -273632, -306819

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 (1,1,-2).

Crossrefs

Cf. A077948.

Programs

GAP

a:=[1,0,1];; for n in [4..60] do a[n]:=a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 28 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1-x-x^2+2*x^3) )); // G. C. Greubel, Jun 28 2019

Mathematica

CoefficientList[Series[(1-x)/(1-x-x^2+2x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {1,1,-2},{1,0,1},60] (* Harvey P. Dale, May 04 2013 *)

PARI

my(x='x+O('x^60)); Vec((1-x)/(1-x-x^2+2*x^3)) \\ G. C. Greubel, Jun 28 2019

Sage

((1-x)/(1-x-x^2+2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jun 28 2019

Formula

a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) - 2*a(n-3). - Harvey P. Dale, May 04 2013

a(n) = A077948(n) - A077948(n-1). - R. J. Mathar, Nov 07 2015