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

Author

Clark Kimberling, Jul 07 2014

Keywords

• nonn

Comments

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

Examples

			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
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A232559, A000045.

Programs

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}]

PARI

\\ See Links section.

Extensions

More terms from Rémy Sigrist, Feb 13 2023