|
|
A003006
|
|
Number of n-level ladder expressions with A001622.
(Formerly M0845)
|
|
1
|
|
|
1, 1, 2, 3, 7, 15, 35, 81, 195, 473, 1170, 2920, 7378, 18787, 48242, 124658, 324095, 846872, 2223352, 5861011, 15508423, 41173560, 109648734
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Number of distinct values taken by phi^phi^...^phi (with n phi's and parentheses inserted in all possible ways), where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - Vladimir Reshetnikov, Mar 05 2019
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
MATHEMATICA
|
ClearAll[phi, t, a]; t[1] = {0}; t[n_Integer] := t[n] = DeleteDuplicates[Flatten[Table[Outer[phi^#1 + #2 &, t[k], t[n - k]], {k, n - 1}]] /. phi^k_Integer :> Fibonacci[k] phi + Fibonacci[k - 1]]; a[n_Integer] := a[n] = Length[t[n]]; Table[a[n], {n, 23}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more,hard
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|