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Expansion of (1-x)^(-1)/(1 + x - x^2 + 2*x^3).
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%I #15 Sep 03 2019 02:29:26

%S 1,0,2,-3,6,-12,25,-48,98,-195,390,-780,1561,-3120,6242,-12483,24966,

%T -49932,99865,-199728,399458,-798915,1597830,-3195660,6391321,

%U -12782640,25565282,-51130563,102261126,-204522252,409044505,-818089008,1636178018,-3272356035,6544712070

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

%C Convolution of A010892(n) and (-1)^n*A001045(n+1). The positive sequence has g.f. 1/((1-x-2x^2)*(1+x+x^2)). This is the convolution of A001045(n+1) and A049347(n). - _Paul Barry_, May 19 2004

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,-3,2)

%F G.f.: 1/((1+x-2x^2)*(1-x+x^2));

%F a(n) = Sum_{k=0..n} (2*(-2)^k/3 + 1/3)*2*sin(Pi*(n-k)/3 + Pi/3)/sqrt(3);

%F a(n) = 2^(n+3)*cos(Pi*n)/21 + 8*sqrt(3)*cos(Pi*n/3 + Pi/6)/63 + 4*sqrt(3)*sin(Pi*n/3 + Pi/3)/63 + 2*sqrt(3)*sin(Pi*n/3)/9 + 1/3. - _Paul Barry_, May 19 2004

%F a(n) = 1/3 + (-1)^n*2^(n+3)/21 - A117373(n+1)/7. - _R. J. Mathar_, Sep 27 2012

%t CoefficientList[Series[(1-x)^(-1)/(1+x-x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{0,2,-3,2},{1,0,2,-3},40] (* _Harvey P. Dale_, Apr 25 2016 *)

%K sign

%O 0,3

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