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%I #40 Feb 21 2024 01:46:07
%S 2,1,8,4,32,16,128,64,512,256,2048,1024,8192,4096,32768,16384,131072,
%T 65536,524288,262144,2097152,1048576,8388608,4194304,33554432,
%U 16777216,134217728,67108864,536870912,268435456,2147483648,1073741824
%N a(n) = 4*a(n-2).
%H Vincenzo Librandi, <a href="/A135520/b135520.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4).
%F From _R. J. Mathar_, corrected Apr 14 2008: (Start)
%F O.g.f.: (5/(1-2*x) + 3/(1+2*x))/4.
%F a(n) = (5*2^n + 3*(-2)^n)/4.
%F a(2*n)=2*A000302(n). a(2*n+1)=A000302(n). (End)
%F a(n) = A000079(n) terms swapped by pairs. - _Paul Curtz_, Apr 26 2011
%F a(n) = 2^(n+(-1)^n). - _Wesley Ivan Hurt_, Dec 13 2013
%F E.g.f.: (1/4)*(5*exp(2*x) + 3*exp(-2*x)). - _G. C. Greubel_, Oct 17 2016
%p A135520:=n->2^(n+(-1)^n); seq(A135520(n), n=0..50); # _Wesley Ivan Hurt_, Dec 13 2013
%t LinearRecurrence[{1,4,-4},{2,1,8},40] (* _Harvey P. Dale_, May 25 2012 *)
%t LinearRecurrence[{0, 4},{2, 1},32] (* _Ray Chandler_, Aug 03 2015 *)
%o (PARI) a(n)=1<<(n+(-1)^n) \\ _Charles R Greathouse IV_, Jun 01 2011
%o (Magma) [(5/4)*2^n+(3/4)*(-2)^n: n in [0..40]]; // _Vincenzo Librandi_, Jun 02 2011
%Y Cf. A097163, A097164.
%K nonn,easy,less
%O 0,1
%A _Paul Curtz_, Feb 19 2008
%E More terms from _R. J. Mathar_, Feb 23 2008
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