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%I #14 Sep 08 2022 08:45:48
%S 1,2,-4,-24,-48,-160,-448,-896,-2304,-5632,-11264,-26624,-61440,
%T -122880,-278528,-622592,-1245184,-2752512,-6029312,-12058624,
%U -26214400,-56623104,-113246208,-243269632,-520093696,-1040187392,-2214592512
%N Expansion of (1-8x^2-24x^3)/((1-2x)^2*(1+2x+4x^2)).
%C Hankel transform of A168055.
%H G. C. Greubel, <a href="/A168054/b168054.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 (2,0,8,-16).
%F a(n) = 2^n*A168053(n).
%F a(n) = 2*a(n-1) + 8*a(n-3) - 16*a(n-4) for n>3. - _Vincenzo Librandi_, Jul 08 2016
%t LinearRecurrence[{2, 0, 8, -16}, {1, 2, -4, -24}, 100] (* _G. C. Greubel_, Jul 07 2016 *)
%t CoefficientList[Series[(1 - 8 x^2 - 24 x^3) / ((1 - 2 x)^2 (1 + 2 x + 4 x^2)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 08 2016 *)
%o (Magma) I:=[1,2,-4,-24]; [n le 4 select I[n] else 2*Self(n-1)+8*Self(n-3)-16*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jul 08 2016
%Y Cf. A168053, A168055.
%K easy,sign
%O 0,2
%A _Paul Barry_, Nov 17 2009