A077955 Expansion of 1/(1-x+2*x^2+x^3).

1, 1, -1, -4, -3, 6, 16, 7, -31, -61, -6, 147, 220, -68, -655, -739, 639, 2772, 2233, -3950, -11188, -5521, 20805, 43035, 6946, -99929, -156856, 36056, 449697, 534441, -401009, -1919588, -1652011, 2588174, 7811784, 4287447, -13924295, -30310973, -6749830, 67796411, 111607044, -17235948

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,-2,-1).

Crossrefs

Cf. A077978.

Programs

GAP

a:=[1,1,-1];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jul 02 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+2*x^2+x^3) )); // G. C. Greubel, Jul 02 2019

Mathematica

LinearRecurrence[{1,-2,-1}, {1,1,-1}, 50] (* or *) CoefficientList[ Series[1/(1-x+2*x^2+x^3), {x,0,50}], x] (* G. C. Greubel, Jul 02 2019 *)

PARI

Vec(1/(1-x+2*x^2+x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

(1/(1-x+2*x^2+x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jul 02 2019

Formula

a(n) = (-1)^n * A077978(n). - G. C. Greubel, Jul 02 2019