%I #14 Sep 08 2022 08:45:40

%S 1,0,4,2,16,8,64,32,256,128,1024,512,4096,2048,16384,8192,65536,32768,

%T 262144,131072,1048576,524288,4194304,2097152,16777216,8388608,

%U 67108864,33554432,268435456,134217728,1073741824,536870912,4294967296,2147483648,17179869184,8589934592,68719476736,34359738368,274877906944

%N Powers of 4 at even indices, two times powers of 4 at odd indices.

%H G. C. Greubel, <a href="/A154383/b154383.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 a(2n) = A131577(2n+1); a(2n+1) = A131577(2n) (Consecutive terms of A131577 swapped).

%F a(2n) = A000302(n); a(2n+1) = A000302(n)/2, n>0.

%F a(n) = 4*a(n-2), n>3.

%F a(2n+1) = a(2n)/2, n>0.

%F G.f.: (1 + 2*x^3)/((1-2*x)*(2*x+1)). - _R. J. Mathar_, May 21 2009

%F a(n) = (5 + 3*(-1)^n)*2^(n-3), n>1. - _R. J. Mathar_, May 21 2009

%F E.g.f.: (1/4)*(-2*x + sinh(2*x) + 4*cosh(2*x)). - _G. C. Greubel_, Sep 15 2016

%t Join[{1, 0}, Table[(5 + 3*(-1)^n)*2^(n - 3), {n, 2, 20}]] (* _G. C. Greubel_, Sep 15 2016 *)

%o (Magma) [1,0] cat [(5+3*(-1)^n)*2^(n-3): n in [2..40]]; // _Vincenzo Librandi_, Sep 16 2016

%K nonn,easy

%O 0,3

%A _Paul Curtz_, Jan 08 2009

%E Edited by _R. J. Mathar_, May 21 2009