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A286390 a(n) = a(n-2) - 2*a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=2, a(2)=-1, a(3)=3.

%I A286390 #15 May 11 2017 06:24:09
%S A286390 0,2,-1,3,-5,7,-12,20,-31,51,-83,133,-216,350,-565,915,-1481,2395,
%T A286390 -3876,6272,-10147,16419,-26567,42985,-69552,112538,-182089,294627,
%U A286390 -476717,771343,-1248060,2019404,-3267463,5286867,-8554331,13841197,-22395528,36236726
%N A286390 a(n) = a(n-2) - 2*a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=2, a(2)=-1, a(3)=3.
%H A286390 Colin Barker, <a href="/A286390/b286390.txt">Table of n, a(n) for n = 0..1000</a>
%H A286390 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,-2,1).
%F A286390 a(n) = A286311(-n).
%F A286390 b(n) = A286311(n) + (period 6 sequence : repeat [0, 1, 0, 0, 0, -1]) = 0, 2, 1, 3, 5, 7, 12, 20, 31, 51, 83, 133,  ... . See A134667(n).
%F A286390 a(n) = -(-1)^n*b(n).
%F A286390 G.f.: x*(2 - x + x^2) / ((1 + x - x^2)*(1 - x + x^2)). - _Colin Barker_, May 08 2017
%t A286390 LinearRecurrence[{0, 1, -2, 1}, {0, 2, -1, 3}, 38] (* or *)
%t A286390 CoefficientList[Series[x (2 - x + x^2)/((1 + x - x^2) (1 - x + x^2)), {x, 0, 37}], x] (* _Michael De Vlieger_, May 08 2017 *)
%o A286390 (PARI) concat(0, Vec(x*(2 - x + x^2) / ((1 + x - x^2)*(1 - x + x^2)) + O(x^60))) \\ _Colin Barker_, May 08 2017
%Y A286390 Cf. A134667, A286311.
%K A286390 sign,easy
%O A286390 0,2
%A A286390 _Paul Curtz_, May 08 2017
%E A286390 Typo in data fixed and more terms added by _Colin Barker_, May 08 2017