OFFSET
1,4
COMMENTS
Generation n consists of F(n) = A000045(n) distinct Fibonacci numbers. Is {a(n)} bounded above?
LINKS
Rémy Sigrist, PARI program
EXAMPLE
In the table below, g(n) denotes generation n of the tree at A232559.
n ... g(n) ............ a(n)
1 ... {1} ............. 1
2 ... {2} ............. 1
3 ... {3,4} ........... 1
4 ... {5,6,8} ......... 2
5 ... {7,9,10,12,16} .. 0
MATHEMATICA
z = 32; g[1] = {1}; f1[x_] := f1[x] = x + 1; f2[x_] := f2[x] = 2 x; h[1] = g[1]; b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]]; h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]; f = Table[Fibonacci[n], {n, 1, 90}]; Table[Length[Intersection[g[n], f]], {n, 1, z}]
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 07 2014
EXTENSIONS
More terms from Rémy Sigrist, Feb 13 2023
STATUS
approved