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A166472 a(n) = 2^F(n+2)*3^F(n+1)/12, where F(n) is the n-th Fibonacci number (A000045(n)).

%I A166472 #13 Jul 30 2024 03:05:22
%S A166472 1,6,72,5184,4478976,278628139008,14975624970497949696,
%T A166472 50071566192138943522512952098816,
%U A166472 8998235963747242817865410245394871488270255869919232
%N A166472 a(n) = 2^F(n+2)*3^F(n+1)/12, where F(n) is the n-th Fibonacci number (A000045(n)).
%H A166472 G. C. Greubel, <a href="/A166472/b166472.txt">Table of n, a(n) for n = 1..15</a>
%F A166472 a(n) = A166470(n+1)/12.
%F A166472 a(n) = 12*a(n-1)*a(n-2), for n > 1, with a(0) = 1/2, a(1) = 1.
%F A166472 A166469(A002110(m)*a(n)) = Fibonacci(m+n+1), for m > 1.
%F A166472 A166469(a(n)) = Fibonacci(n+3) - 2 = A001911(n).
%t A166472 Table[(2^Fibonacci[n+2]*3^Fibonacci[n+1])/12, {n,12}] (* _G. C. Greubel_, May 15 2016 *)
%t A166472 (3^#[[1]] 2^#[[2]])/12&/@Partition[Fibonacci[Range[2,15]],2,1] (* _Harvey P. Dale_, Jul 12 2021 *)
%o A166472 (Magma) [2^(Fibonacci(n+2)-2)*3^(Fibonacci(n+1)-1): n in [1..12]]; // _G. C. Greubel_, Jul 30 2024
%o A166472 (SageMath) [2^(fibonacci(n+2)-2)*3^(fibonacci(n+1)-1) for n in range(1,13)] # _G. C. Greubel_, Jul 30 2024
%Y A166472 Cf. A000045, A001911, A002110, A166469, A166470, A166471, A166473.
%Y A166472 Subsequence of A003586, A025487.
%K A166472 nonn
%O A166472 1,2
%A A166472 _Matthew Vandermast_, Nov 05 2009