A077869 - OEIS

%I #17 Jan 25 2022 21:16:20

%S 1,2,3,3,2,0,-2,-3,-2,1,5,8,8,4,-3,-10,-13,-9,2,16,26,25,10,-15,-39,

%T -48,-32,8,57,90,83,27,-62,-144,-170,-107,38,209,317,280,72,-244,-523,

%U -594,-349,175,770,1120,946,177,-942,-1887,-2063,-1120,768,2832,3953,3186,355,-3597,-6782,-7136,-3538,3245

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-1,1).

%F a(n) = Sum_{k=0..floor((n+1)/2)} (-1)^k*binomial(n+1-2k,k+1), n>=0. - _Taras Goy_, Apr 15 2020

%F From _Wesley Ivan Hurt_, Jan 25 2022: (Start)

%F G.f.: (1-x)^(-1)/(1-x+x^3).

%F a(n) = 2*a(n-1)-a(n-2)-a(n-3)+a(n-4). (End)

%t CoefficientList[Series[(1/(1-x))/(1-x+x^3),{x,0,70}],x] (* _Harvey P. Dale_, Mar 20 2013 *)

%K sign

%O 0,2

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