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%I #18 Sep 08 2022 08:45:32
%S 0,1,3,8,18,40,84,176,360,736,1488,3008,6048,12160,24384,48896,97920,
%T 196096,392448,785408,1571328,3143680,6288384,12578816,25159680,
%U 50323456,100651008,201310208,402628608,805273600,1610563584,3221159936
%N a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) with n>2, a(0)=0, a(1)=1, a(2)=3.
%H G. C. Greubel, <a href="/A135094/b135094.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-4).
%F From _R. J. Mathar_, Feb 15 2008: (Start)
%F O.g.f.: -3/(2*(2*x-1)) + (4*x+3)/(2*(2*x^2-1)).
%F a(n) = 3*2^(n-1) - A063759(n+1)/2. (End)
%F From _Colin Barker_, Sep 23 2016: (Start)
%F a(n) = 3*2^(n-1) - 3*2^(n/2-1) for n even.
%F a(n) = 3*2^(n-1) - 2^((n+1)/2) for n odd. (End)
%t LinearRecurrence[{2, 2, -4}, {0, 1, 3}, 50] (* _G. C. Greubel_, Sep 22 2016 *)
%o (Magma) I:=[0,1,3]; [n le 3 select I[n] else 2*Self(n-1)+2*Self(n-2)-4*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Sep 23 2016
%Y Cf. A026635, A026657.
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Feb 12 2008
%E More terms from _R. J. Mathar_, Feb 15 2008
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