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Expansion of (1+x+x^2+x^3)/(1-x^2+x^4).
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%I #13 Dec 14 2023 05:20:44

%S 1,1,2,2,1,1,-1,-1,-2,-2,-1,-1,1,1,2,2,1,1,-1,-1,-2,-2,-1,-1,1,1,2,2,

%T 1,1,-1,-1,-2,-2,-1,-1,1,1,2,2,1,1,-1,-1,-2,-2,-1,-1,1,1,2,2,1,1,-1,

%U -1,-2,-2,-1,-1,1,1,2,2,1,1,-1,-1,-2,-2,-1,-1

%N Expansion of (1+x+x^2+x^3)/(1-x^2+x^4).

%C Periodic{1,1,2,2,1,1,-1,-1,-2,-2,-1,-1}.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1).

%F G.f.: (1-x^4)/(1-x-x^2+x^3+x^4-x^5); a(n)=cos(5*pi*n/6)/2+(1-sqrt(3)/2)sin(5*pi*n/6)+cos(pi*n/6)/2+(1+sqrt(3)/2)sin(pi*n/6);

%t CoefficientList[Series[(1+x+x^2+x^3)/(1-x^2+x^4),{x,0,100}],x] (* or *) LinearRecurrence[{0,1,0,-1},{1,1,2,2},100] (* _Harvey P. Dale_, Aug 02 2015 *)

%Y Cf. A128017.

%K easy,sign

%O 0,3

%A _Paul Barry_, Feb 11 2007