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

%I #17 May 10 2024 10:58:48

%S 1,2,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,

%T -1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,

%U 0,-1,1,0,-1,1,0,-1,1,0

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

%C Row sums of number triangle A122433. Binomial transform is A077859.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1).

%F a(n) = 2*sqrt(3)*cos(2*Pi*n/3+Pi/6)/3+C(1,n)+C(0,n).

%F a(n) = -A049347(n) if n>=2 . - _R. J. Mathar_, Feb 08 2008

%t CoefficientList[Series[(1+x)^3/(1+x+x^2),{x,0,70}],x] (* or *) PadRight[ {1,2,0},71,{-1,1,0}] (* _Harvey P. Dale_, Apr 25 2012 *)

%K easy,sign

%O 0,2

%A _Paul Barry_, Sep 04 2006