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A163864 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.

%I A163864 #8 Sep 08 2022 08:45:47
%S A163864 1,6,2,12,4,24,8,48,16,96,32,192,64,384,128,768,256,1536,512,3072,
%T A163864 1024,6144,2048,12288,4096,24576,8192,49152,16384,98304,32768,196608,
%U A163864 65536,393216,131072,786432,262144,1572864,524288,3145728,1048576,6291456
%N A163864 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
%C A163864 Interleaving of A000079 and A007283 without initial 3.
%C A163864 Binomial transform is A048694, second binomial transform is A163613, third binomial transform is A163614, fourth binomial transform is A163615, fifth binomial transform is A163616, sixth binomial transform is A081183 without initial 0.
%H A163864 Vincenzo Librandi, <a href="/A163864/b163864.txt">Table of n, a(n) for n = 1..2000</a>
%H A163864 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A163864 a(n) = (2+(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).
%F A163864 G.f.: x*(1+6*x)/(1-2*x^2).
%t A163864 LinearRecurrence[{0, 2}, {1, 6, 2, 12}, 50] (* _G. C. Greubel_, Aug 06 2017 *)
%o A163864 (Magma) [ n le 2 select 5*n-4 else 2*Self(n-2): n in [1..42] ];
%o A163864 (PARI) x='x+O('x^50); Vec(x*(1+6*x)/(1-2*x^2)) \\ _G. C. Greubel_, Aug 06 2017
%Y A163864 Cf. A000079 (powers of 2), A007283 (3*2^n), A048694, A163613, A163614, A163615, A163616, A081183.
%K A163864 nonn
%O A163864 1,2
%A A163864 _Klaus Brockhaus_, Aug 05 2009