A078015 Expansion of (1-x)/(1-x+x^2-2*x^3).

1, 0, -1, 1, 2, -1, -1, 4, 3, -3, 2, 11, 3, -4, 15, 25, 2, 7, 55, 52, 11, 69, 162, 115, 91, 300, 439, 321, 482, 1039, 1199, 1124, 2003, 3277, 3522, 4251, 7283, 10076, 11295, 15785, 24642, 31447, 38375, 56212, 80731, 101269, 132962, 193155, 262731, 335500, 459079, 649041

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,-1,2).

Crossrefs

Cf. A077951.

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 29 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1-x+x^2-2*x^3) )); // G. C. Greubel, Jun 29 2019

Mathematica

LinearRecurrence[{1,-1,2}, {1,0,-1}, 60] (* or *) CoefficientList[Series[ (1-x)/(1-x+x^2-2*x^3), {x,0,60}], x] (* G. C. Greubel, Jun 29 2019 *)

PARI

my(x='x+O('x^60)); Vec((1-x)/(1-x+x^2-2*x^3)) \\ G. C. Greubel, Jun 29 2019

Sage

((1-x)/(1-x+x^2-2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019

Formula

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

a(n) = A077951(n) - A077951(n-1). - G. C. Greubel, Jun 29 2019