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%I #12 Aug 10 2017 03:18:24
%S 1,3,5,2,-6,-11,-5,9,17,8,-12,-23,-11,15,29,14,-18,-35,-17,21,41,20,
%T -24,-47,-23,27,53,26,-30,-59,-29,33,65,32,-36,-71,-35,39,77,38,-42,
%U -83,-41,45,89,44,-48,-95,-47,51,101
%N Expansion of (1 + x + 2*x^2 - x^3)/(1 - 2*x + 3*x^2 - 2*x^3 + x^4).
%C Hankel transform of A113682.
%H G. C. Greubel, <a href="/A164611/b164611.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,2,-1).
%F G.f.: (1+x+2*x^2-x^3)/(1-x+x^2)^2.
%F a(n) = 2*a(n-1)-3*a(n-2)+2*a(n-3)-a(n-4), with a(0)=1, a(1)=3, a(2)=5, a(3)=2. - _Harvey P. Dale_, May 28 2013
%t CoefficientList[Series[(1+x+2x^2-x^3)/(1-2x+3x^2-2x^3+x^4),{x,0,80}],x] (* or *) LinearRecurrence[{2,-3,2,-1},{1,3,5,2},80] (* _Harvey P. Dale_, May 28 2013 *)
%o (PARI) x='x+O('x^50); Vec((1 +x +2*x^2 -x^3)/(1 -2*x +3*x^2 -2*x^3 +x^4)) \\ _G. C. Greubel_, Aug 10 2017
%K easy,sign
%O 0,2
%A _Paul Barry_, Aug 17 2009
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