A078016 Expansion of (1-x)/(1-x+x^2+x^3).

1, 0, -1, -2, -1, 2, 5, 4, -3, -12, -13, 2, 27, 38, 9, -56, -103, -56, 103, 262, 215, -150, -627, -692, 85, 1404, 2011, 522, -2893, -5426, -3055, 5264, 13745, 11536, -7473, -32754, -36817, 3410, 72981, 106388, 29997, -149372, -285757, -166382, 268747, 720886, 618521, -371112, -1710519

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign

Links

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

Programs

GAP

a:=[1,0,-1];; for n in [4..50] do a[n]:=a[n-1]-a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jun 29 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+x^2+x^3) )); // G. C. Greubel, Jun 29 2019

Mathematica

CoefficientList[Series[(1-x)/(1-x+x^2+x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {1,-1,-1},{1,0,-1},50] (* Harvey P. Dale, Nov 08 2011 *)

PARI

my(x='x+O('x^50)); Vec((1-x)/(1-x+x^2+x^3)) \\ G. C. Greubel, Jun 29 2019

Sage

((1-x)/(1-x+x^2+x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019

Formula

G.f.: (1-x)/(1-x+x^2+x^3).

a(0)=1, a(1)=0, a(2)=-1, a(n) = a(n-1) - a(n-2) - a(n-3). - Harvey P. Dale, Nov 08 2011