A077978 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
• Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019.
• Index entries for linear recurrences with constant coefficients, signature (-1,-2,1).

Crossrefs

Cf. A077955, A077911, A078049.

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, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x+2*x^2-x^3) )); // G. C. Greubel, Jun 25 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, Jun 25 2019 *)

PARI

Vec(1/(1+x+2*x^2-x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1+x+2*x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(n) = (-1)^n * A077955(n). - G. C. Greubel, Jun 25 2019

Extensions

Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021