A077975 - OEIS

%I #18 Sep 08 2022 08:45:08

%S 1,-1,0,3,-5,2,9,-21,16,23,-81,90,37,-289,432,-69,-941,1874,-1071,

%T -2685,7504,-6961,-5913,27882,-35891,-3817,95472,-163437,60331,294050,

%U -681255,507867,761488,-2631865,2886111,1268730,-9418571,13922063,-1966032,-30793173,60603331,-33742222,-88447455

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

%H G. C. Greubel, <a href="/A077975/b077975.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,2).

%F Recurrence: a(n) = 2a(n-3) - a(n-2) - a(n-1), starting 1,-1,0. - _Ralf Stephan_, Aug 18 2013

%t 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 *)

%o (PARI) Vec(1/(1+x+x^2-2*x^3)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x+x^2-2*x^3) )); // _G. C. Greubel_, Jun 25 2019

%o (Sage) (1/(1+x+x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 25 2019

%o (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

%K sign,easy

%O 0,4

%A _N. J. A. Sloane_, Nov 17 2002