%I #13 May 29 2024 20:03:19
%S 1,2,-1,-1,-5,1,1,8,-1,-1,-11,1,1,14,-1,-1,-17,1,1,20,-1,-1,-23,1,1,
%T 26,-1,-1,-29,1,1,32,-1,-1,-35,1,1,38,-1,-1,-41,1,1,44,-1,-1,-47,1,1,
%U 50,-1,-1,-53,1,1,56,-1,-1,-59,1,1,62,-1,-1,-65,1,1,68,-1,-1
%N Expansion of g.f. (1+2*x-x^2+x^3-x^4-x^5)/(1+x^3)^2.
%C Hankel transform of A174783.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-2,0,0,-1).
%F a(n) = (n+4)*cos(pi*n/3)/3 + n*sin(pi*n/3)/sqrt(3) - (n+1)*(-1)^n/3.
%F E.g.f.: exp(-x)*(2*exp(3*x/2)*(2 + x)*cos(sqrt(3)*x/2) + x - 1)/3. - _Stefano Spezia_, May 29 2024
%t CoefficientList[Series[(1+2x-x^2+x^3-x^4-x^5)/(1+x^3)^2,{x,0,50}],x] (* or *) LinearRecurrence[{0,0,-2,0,0,-1},{1,2,-1,-1,-5,1},60] (* _Harvey P. Dale_, May 11 2019 *)
%Y Cf. A174783.
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 29 2010
%E a(51)-a(69) from _Stefano Spezia_, May 29 2024