A166470 a(n) = 2^F(n+1)*3^F(n), where F(n) is the n-th Fibonacci number, A000045(n).

2, 6, 12, 72, 864, 62208, 53747712, 3343537668096, 179707499645975396352, 600858794305667322270155425185792, 107978831564966913814384922944738457859243070439030784

Offset: 0

Author

Matthew Vandermast, Nov 05 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..16

Crossrefs

Subsequence of A025610 and hence of A003586 and A025487.

Cf. A000045, A000301, A002110, A010098, A115033, A166469, A174666, A230900.

Programs

Magma

[2^Fibonacci(n+1)*3^Fibonacci(n): n in [0..14]]; // G. C. Greubel, Jul 29 2024

Mathematica

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

PARI

a(n)=2^fibonacci(n+1)*3^fibonacci(n) \\ Charles R Greathouse IV, Sep 19 2022

SageMath

[2^fibonacci(n+1)*3^fibonacci(n) for n in range(15)] # G. C. Greubel, Jul 29 2024

Formula

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

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

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

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

a(n) = 2 * A174666(n+1). - Alois P. Heinz, Sep 16 2022

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

a(n) = A115033(2*n+1). - David Radcliffe, May 31 2025

Extensions

Typo corrected by Matthew Vandermast, Nov 07 2009