A244860 Number of Fibonacci numbers in generation n of the tree at A232559.

1, 1, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 2, 0, 0, 2, 0, 1, 1, 1, 2, 1, 0, 0, 3, 2, 0, 1, 1, 0, 0, 1, 1, 0, 4, 1, 0, 1, 0, 0, 1, 4, 2, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 3, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2

Offset

1,4

Comments

Generation n consists of F(n) = A000045(n) distinct Fibonacci numbers. Is {a(n)} bounded above?

Links

Table of n, a(n) for n=1..87.

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

Cf. A232559, A000045.

Sequence in context: A166124 A134979 A112248 * A308009 A010872 A220663

Adjacent sequences: A244857 A244858 A244859 * A244861 A244862 A244863

Keyword

nonn

Author

Clark Kimberling, Jul 07 2014

Extensions

More terms from Rémy Sigrist, Feb 13 2023

Status

approved