A244860 - OEIS

%I #11 Feb 13 2023 08:57:26

%S 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,

%T 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,

%U 1,2,1,0,2,3,0,1,0,0,1,0,3,0,1,0,1,1,2

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

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

%H Rémy Sigrist, <a href="/A244860/a244860.gp.txt">PARI program</a>

%e In the table below, g(n) denotes generation n of the tree at A232559.

%e n ... g(n) ............ a(n)

%e 1 ... {1} ............. 1

%e 2 ... {2} ............. 1

%e 3 ... {3,4} ........... 1

%e 4 ... {5,6,8} ......... 2

%e 5 ... {7,9,10,12,16} .. 0

%t 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}]

%o (PARI) See Links section.

%Y Cf. A232559, A000045.

%K nonn

%O 1,4

%A _Clark Kimberling_, Jul 07 2014

%E More terms from _Rémy Sigrist_, Feb 13 2023