cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

2, 6, 12, 72, 864, 62208, 53747712, 3343537668096, 179707499645975396352, 600858794305667322270155425185792, 107978831564966913814384922944738457859243070439030784
Offset: 0

Views

Author

Matthew Vandermast, Nov 05 2009

Keywords

Links

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

A174677 a(n) = 2*a(n-1)*a(n-2) with a(0)=1 and a(1)=1.

Original entry on oeis.org

1, 1, 2, 4, 16, 128, 4096, 1048576, 8589934592, 18014398509481984, 309485009821345068724781056, 11150372599265311570767859136324180752990208
Offset: 0

Views

Author

Giovanni Teofilatto, Mar 26 2010

Keywords

Comments

a(n) is the number of node minimal AVL trees of height n. - Alois P. Heinz, Mar 13 2013

Links

Crossrefs

Cf. A000045, A000301, A143897, A174666, A217298.

Programs

Formula

a(n) = 2^(Fibonacci(n+1) - 1).
a(n) = 1/2 * A000301(n+1).

Extensions

Formula index corrected by R. J. Mathar, Mar 30 2010
a(0)=1 prepended and name edited by Alois P. Heinz, Jul 05 2021
Showing 1-2 of 2 results.

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