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A286350 a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=0, a(1)=a(2)=2, a(3)=3.

%I A286350 #22 Sep 08 2022 08:46:19
%S A286350 0,2,2,3,4,7,12,20,32,51,82,133,216,350,566,915,1480,2395,3876,6272,
%T A286350 10148,16419,26566,42985,69552,112538,182090,294627,476716,771343,
%U A286350 1248060,2019404,3267464,5286867,8554330,13841197,22395528,36236726,58632254,94868979
%N A286350 a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=0, a(1)=a(2)=2, a(3)=3.
%C A286350 This is b(n) in A286311(n). As mentioned in A286311, the pair A286311(n) and, here a(n), are autosequences of the first kind.
%H A286350 Colin Barker, <a href="/A286350/b286350.txt">Table of n, a(n) for n = 0..1000</a>
%H A286350 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1).
%F A286350 a(n) = A286311(n) + A128834(n).
%F A286350 a(n) = A022086(n) - A286311(n).
%F A286350 a(n) = (A022086(n) + A128834(n))/2.
%F A286350 G.f.: x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)). - _Colin Barker_, May 09 2017
%t A286350 LinearRecurrence[{2, -1, 0, 1}, {0, 2, 2, 3}, 40] (* or *)
%t A286350 CoefficientList[Series[x (2 - 2 x + x^2)/((1 - x + x^2) (1 - x - x^2)), {x, 0, 39}], x] (* _Michael De Vlieger_, May 09 2017 *)
%o A286350 (PARI) concat(0, Vec(x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)) + O(x^60))) \\ _Colin Barker_, May 09 2017
%o A286350 (Magma) I:=[0,2,2,3]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) + Self(n-4): n in [1..30]]; // _G. C. Greubel_, Jan 15 2018
%Y A286350 Cf. A022086, A128834, A226956 (same recurrence), A286311.
%K A286350 nonn,easy
%O A286350 0,2
%A A286350 _Paul Curtz_, May 08 2017
%E A286350 More terms from _Colin Barker_, May 09 2017