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

1, 6, 72, 5184, 4478976, 278628139008, 14975624970497949696, 50071566192138943522512952098816, 8998235963747242817865410245394871488270255869919232

Offset: 1

Author

Matthew Vandermast, Nov 05 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A000045, A001911, A002110, A166469, A166470, A166471, A166473.

Subsequence of A003586, A025487.

Programs

Magma

[2^(Fibonacci(n+2)-2)*3^(Fibonacci(n+1)-1): n in [1..12]]; // G. C. Greubel, Jul 30 2024

Mathematica

Table[(2^Fibonacci[n+2]*3^Fibonacci[n+1])/12, {n,12}] (* G. C. Greubel, May 15 2016 *)
(3^#[[1]] 2^#[[2]])/12&/@Partition[Fibonacci[Range[2,15]],2,1] (* Harvey P. Dale, Jul 12 2021 *)

SageMath

[2^(fibonacci(n+2)-2)*3^(fibonacci(n+1)-1) for n in range(1,13)] # G. C. Greubel, Jul 30 2024

Formula

a(n) = A166470(n+1)/12.

a(n) = 12*a(n-1)*a(n-2), for n > 1, with a(0) = 1/2, a(1) = 1.

A166469(A002110(m)*a(n)) = Fibonacci(m+n+1), for m > 1.

A166469(a(n)) = Fibonacci(n+3) - 2 = A001911(n).