A077911 Expansion of 1/((1-x)*(1+x+2*x^2-x^3)).

1, 0, -1, 3, 0, -6, 10, 3, -28, 33, 27, -120, 100, 168, -487, 252, 891, -1881, 352, 4302, -6886, -1365, 19440, -23595, -16649, 83280, -73576, -109632, 340065, -194376, -595385, 1324203, -327808, -2915982, 4895802, 608355, -13315940, 16995033, 10245203, -57551208, 54055836, 71291784

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,-1,3,-1).

Crossrefs

Cf. A077978.

Programs

GAP

a:=[1,0,-1,3];; for n in [4..50] do a[n]:=-a[n-2]+3*a[n-3]-a[n-4]; od; a; # G. C. Greubel, Jul 02 2019

Magma

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

Mathematica

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

PARI

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

Sage

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