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A164587 a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.

%I A164587 #9 Jun 30 2023 01:04:42
%S A164587 1,8,2,16,4,32,8,64,16,128,32,256,64,512,128,1024,256,2048,512,4096,
%T A164587 1024,8192,2048,16384,4096,32768,8192,65536,16384,131072,32768,262144,
%U A164587 65536,524288,131072,1048576,262144,2097152,524288,4194304,1048576
%N A164587 a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.
%C A164587 Interleaving of A000079 and A000079 without initial terms 1, 2, 4.
%C A164587 Binomial transform is A048696. Second binomial transform is A164298.
%H A164587 G. C. Greubel, <a href="/A164587/b164587.txt">Table of n, a(n) for n = 1..1000</a>
%H A164587 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2).
%F A164587 a(n) = (5 + 3*(-1)^n)*2^((2*n -5 +(-1)^n)/4).
%F A164587 G.f.: x*(1+8*x)/(1-2*x^2).
%F A164587 E.g.f.: 4*cosh(sqrt(2)*x) + (1/sqrt(2))*sinh(sqrt(2)*x) - 4. - _G. C. Greubel_, Aug 12 2017
%t A164587 CoefficientList[Series[(1 - x)/(1 - 10*x + 17*x^2), {x,0,50}], x] (* _G. C. Greubel_, Aug 12 2017 *)
%o A164587 (Magma) [ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];
%o A164587 (PARI) x='x+O('x^50); Vec(x*(1+8*x)/(1-2*x^2)) \\ _G. C. Greubel_, Aug 12 2017
%Y A164587 Equals A112032 without initial term 4.
%Y A164587 Cf. A000079 (powers of 2), A048696, A164298.
%K A164587 nonn
%O A164587 1,2
%A A164587 _Klaus Brockhaus_, Aug 17 2009