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%I #27 Mar 23 2023 06:23:54
%S 1,-2,2,0,-2,4,-2,0,6,-4,6,8,-2,20,14,16,54,44,86,152,174,324,478,672,
%T 1126,1628,2470,3880,5726,8820,13486,20272,31126,47244,71670,109496,
%U 166158,252836,385150,585152
%N Expansion of (x-1)^2/(1-x^2-2*x^3).
%C A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj').
%H G. C. Greubel, <a href="/A159286/b159286.txt">Table of n, a(n) for n = 0..1000</a>
%H Creighton Dement, <a href="http://fumba.eu/sitelayout/Floretion.php">Online Floretion Multiplier</a> [broken link].
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2).
%F a(n) = A159288(n) - 3*A159287(n+1). - _R. J. Mathar_, Apr 10 2009
%F a(1)=1, a(2)=-2, a(3)=2, a(n) = 1*a(n-2) + 2*a(n-3) for n >= 3. - _Harvey P. Dale_, Apr 24 2011
%F a(n) = A078026(n)-A078026(n-1). - _R. J. Mathar_, Mar 23 2023
%t CoefficientList[Series[(x-1)^2/(1-x^2-2*x^3),{x,0,40}],x] (* or *) LinearRecurrence[{0,1,2},{1,-2,2},40] (* _Harvey P. Dale_, Apr 24 2011 *)
%o (PARI) a(n)=([0,1,0; 0,0,1; 2,1,0]^n*[1;-2;2])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016
%o (Magma) I:=[1, -2, 2]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Jun 27 2018
%Y Cf. A159284, A159285, A159287, A159288.
%K easy,sign
%O 0,2
%A _Creighton Dement_, Apr 08 2009
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