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

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

Offset: 0

Author

Giovanni Teofilatto, Mar 26 2010

Keywords

• easy
• nonn

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..17

Crossrefs

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

Programs

Magma

[2^(Fibonacci(n+1)-1): n in [0..10]]; // Vincenzo Librandi, Apr 24 2011

Mathematica

2^(Fibonacci[Range[15]] -1) (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
Join[{1}, RecurrenceTable[{a[1]==1,a[2]==2,a[n]==2a[n-1]a[n-2]},a[n],{n, 12}]] (* Harvey P. Dale, Jul 07 2011 *)

SageMath

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

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