A077975 Expansion of 1/(1+x+x^2-2*x^3).

1, -1, 0, 3, -5, 2, 9, -21, 16, 23, -81, 90, 37, -289, 432, -69, -941, 1874, -1071, -2685, 7504, -6961, -5913, 27882, -35891, -3817, 95472, -163437, 60331, 294050, -681255, 507867, 761488, -2631865, 2886111, 1268730, -9418571, 13922063, -1966032, -30793173, 60603331, -33742222, -88447455

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,-1,2).

Programs

GAP

a:=[1,-1,0];; for n in [4..50] do a[n]:=-a[n-1]-a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

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

Mathematica

CoefficientList[Series[1/(1+x+x^2-2x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {-1,-1,2},{1,-1,0},50] (* Harvey P. Dale, Jul 20 2015 *)

PARI

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

Sage

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

Formula

Recurrence: a(n) = 2a(n-3) - a(n-2) - a(n-1), starting 1,-1,0. - Ralf Stephan, Aug 18 2013