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A137447 a(n) = 4*a(n-4) for n>3, a(0)=-1, a(1)=-4, a(2)=2, a(3)=12.

%I A137447 #28 Sep 15 2023 01:44:55
%S A137447 -1,-4,2,12,-4,-16,8,48,-16,-64,32,192,-64,-256,128,768,-256,-1024,
%T A137447 512,3072,-1024,-4096,2048,12288,-4096,-16384,8192,49152,-16384,
%U A137447 -65536,32768,196608,-65536,-262144,131072,786432,-262144,-1048576,524288,3145728,-1048576
%N A137447 a(n) = 4*a(n-4) for n>3, a(0)=-1, a(1)=-4, a(2)=2, a(3)=12.
%H A137447 G. C. Greubel, <a href="/A137447/b137447.txt">Table of n, a(n) for n = 0..1000</a>
%H A137447 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4).
%F A137447 G.f.: (1+4*x-2*x^2-12*x^3)/(4*x^4-1). - _Harvey P. Dale_, Jun 27 2011
%F A137447 From _Bruno Berselli_, Nov 02 2011: (Start)
%F A137447 a(n) = (1-(-1)^n-2*(3-2*(-1)^n)*(-1)^floor(n/2))*2^(floor(n/2)-1).
%F A137447 a(2n) = -A122803(n).
%F A137447 a(2n+1) = (-1)^(n+1)*A084221(n+2). (End)
%F A137447 E.g.f.: (1/sqrt(2))*( sinh(sqrt(2)*x) - 5*sin(sqrt(2)*x) - sqrt(2)*cos(sqrt(2)*x) ). - _G. C. Greubel_, Sep 15 2023
%t A137447 LinearRecurrence[{0,0,0,4},{-1,-4,2,12},50] (* or *) CoefficientList[ Series[(1+4x-2x^2-12x^3)/(4x^4-1),{x,0,50}],x] (* _Harvey P. Dale_, Jun 27 2011 *)
%o A137447 (Magma) &cat[[-(-2)^n,2^n-5*(-2)^n]: n in [0..20]];  // _Bruno Berselli_, Nov 02 2011
%o A137447 (SageMath)
%o A137447 def A137447(n): return 2^(n//2)*(-1)^(n//2+1) if n%2==0 else 2^((n-1)//2)*(1 - 5*(-1)^((n-1)//2))
%o A137447 [A137447(n) for n in range(51)] # _G. C. Greubel_, Sep 15 2023
%Y A137447 Cf. A084221, A102561, A122803.
%K A137447 sign,easy
%O A137447 0,2
%A A137447 _Paul Curtz_, Apr 18 2008
%E A137447 More terms from _Harvey P. Dale_, Jun 27 2011