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a(n) = 2^F(n+1)*3^F(n), where F(n) is the n-th Fibonacci number, A000045(n).
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%I #58 Jul 30 2024 03:06:40

%S 2,6,12,72,864,62208,53747712,3343537668096,179707499645975396352,

%T 600858794305667322270155425185792,

%U 107978831564966913814384922944738457859243070439030784

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

%H G. C. Greubel, <a href="/A166470/b166470.txt">Table of n, a(n) for n = 0..16</a>

%F a(n) = A000301(n+1)*A010098(n).

%F For n > 1, a(n) = a(n-1)*a(n-2).

%F For m > 1, n > 1, A166469(A002110(m)*(a(n)^k)/12) = k*Fibonacci(m+n).

%F A166469(a(n)) = Fibonacci(n+2) + 1 = A001611(n+2).

%F a(n) = 2 * A174666(n+1). - _Alois P. Heinz_, Sep 16 2022

%F a(n) = 2^(Fibonacci(n+1) + c*Fibonacci(n)), with c=log_2(3). Cf. A000301 (c=1) & A010098 (c=2). - _Andrea Pinos_, Sep 29 2022

%t 3^First[#] 2^Last[#]&/@Partition[Fibonacci[Range[0,12]],2,1] (* _Harvey P. Dale_, Aug 20 2012 *)

%o (PARI) a(n)=2^fibonacci(n+1)*3^fibonacci(n) \\ _Charles R Greathouse IV_, Sep 19 2022

%o (Magma) [2^Fibonacci(n+1)*3^Fibonacci(n): n in [0..14]]; // _G. C. Greubel_, Jul 29 2024

%o (SageMath) [2^fibonacci(n+1)*3^fibonacci(n) for n in range(15)] # _G. C. Greubel_, Jul 29 2024

%Y Subsequence of A025610 and hence of A003586 and A025487.

%Y Cf. A000045, A000301, A002110, A010098, A166469, A174666, A230900.

%K nonn,easy

%O 0,1

%A _Matthew Vandermast_, Nov 05 2009

%E Typo corrected by _Matthew Vandermast_, Nov 07 2009