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A171648 a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*Fibonacci((n+1)/2)/Fibonacci((n-1)/2) if n is odd.

%I A171648 #21 Aug 02 2016 18:21:21
%S A171648 1,2,2,4,8,16,24,48,80,160,256,512,832,1664,2688,5376,8704,17408,
%T A171648 28160,56320,91136,182272,294912,589824,954368,1908736,3088384,
%U A171648 6176768,9994240,19988480,32342016,64684032,104660992,209321984,338690048,677380096,1096024064
%N A171648 a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*Fibonacci((n+1)/2)/Fibonacci((n-1)/2) if n is odd.
%C A171648 a(n)/a(n-1) apparently tends to phi = A001622 if n=odd; e.g. a(21)/a(20) = 91136/56320 = 1.61818...
%C A171648 a(n)/a(n-2) apparently tends to 1+sqrt(5) = 3.236...= A134945; where a(21)/a(19) = 91136/28160 = 3.23636...
%C A171648 a(1)=1, a(2)=2, a(3)=2, for n>3 a(n)=2*a(n-1) if n is even and a(n)=2*(a(n-1)-a(n-2)+a(n-3)) if n is odd. - _Vincenzo Librandi_, Dec 06 2010
%H A171648 Colin Barker, <a href="/A171648/b171648.txt">Table of n, a(n) for n = 1..1000</a>
%H A171648 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,4).
%F A171648 a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*A000045((n+1)/2)/A000045((n-1)/2) if n is odd.
%F A171648 From _Colin Barker_, Aug 02 2016: (Start)
%F A171648 a(n) = 2*a(n-2) + 4*a(n-4) for n>4.
%F A171648 G.f.: x*(1+2*x) / (1-2*x^2-4*x^4).
%F A171648 (End)
%e A171648 a(8) = 48 = 2*a(7) = 2*24. a(9) = 80 = (5/3)*48 since Fibonacci(5) = 5 and Fibonacci(4) = 3.
%o A171648 (PARI) Vec(x*(1+2*x)/(1-2*x^2-4*x^4) + O(x^50)) \\ _Colin Barker_, Aug 02 2016
%Y A171648 Cf. A063727 (bisection), A103435 (bisection).
%K A171648 nonn,easy
%O A171648 1,2
%A A171648 _Gary W. Adamson_, Dec 13 2009
%E A171648 Defined "F", removed abundant parentheses, added punctuation to examples, added a factor to the definition, corrected a(13) and added more terms - _R. J. Mathar_, Dec 15 2009