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A138377 a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 2; thereafter a(n) = -4*a(n-4).

%I A138377 #16 Jul 14 2022 20:29:10
%S A138377 0,1,3,2,0,-4,-12,-8,0,16,48,32,0,-64,-192,-128,0,256,768,512,0,-1024,
%T A138377 -3072,-2048,0,4096,12288,8192,0,-16384,-49152,-32768,0,65536,196608,
%U A138377 131072,0,-262144,-786432,-524288,0,1048576,3145728,2097152,0,-4194304,-12582912,-8388608,0,16777216,50331648
%N A138377 a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 2; thereafter a(n) = -4*a(n-4).
%C A138377 First and third differences have only 2^n's.
%H A138377 G. C. Greubel, <a href="/A138377/b138377.txt">Table of n, a(n) for n = 0..1000</a>
%H A138377 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, -4).
%F A138377 From _R. J. Mathar_, May 09 2008: (Start)
%F A138377 O.g.f.: x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2)).
%F A138377 a(n) = (5*A009545(n) - A108520(n))/4. (End)
%t A138377 LinearRecurrence[{0,0,0,-4},{0,1,3,2},60] (* _Harvey P. Dale_, Mar 19 2012 *)
%o A138377 (PARI) x='x+O('x^25); Vec(x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2))) \\ _G. C. Greubel_, Feb 20 2017
%Y A138377 Cf. A138380, A138382.
%K A138377 sign,easy
%O A138377 0,3
%A A138377 _Paul Curtz_, May 08 2008