OFFSET
0,3
COMMENTS
a(n) is the number of node minimal AVL trees of height n. - Alois P. Heinz, Mar 13 2013
a(n) counts optimal solutions for the Tower of Fibonacci problem with n disks. - El-Mehdi Mehiri, Mar 28 2026
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..17
El-Mehdi Mehiri, Saad Mneimneh and Hacène Belbachir, The Towers of Fibonacci, Lucas, Jacobsthal, and Pell, and Their Associated Graphs, Fibonacci Quart. (2026). See p. 11.
FORMULA
a(n) = 2^(Fibonacci(n+1) - 1).
a(n) = 1/2 * A000301(n+1).
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 *)
PROG
(Magma) [2^(Fibonacci(n+1)-1): n in [0..10]]; // Vincenzo Librandi, Apr 24 2011
(SageMath) [2^(fibonacci(n+1) -1) for n in range(13)] # G. C. Greubel, Jul 30 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Mar 26 2010
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
STATUS
approved
