A243850 Number of numbers in row n of the array at A243848.

1, 1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 74, 117, 184, 291, 455, 719, 1135, 1789, 2821, 4456, 7025, 11097, 17510, 27645, 43668, 68973, 108897, 172051, 271835, 429442, 678573

Offset

1,4

Comments

Decree that (row 1) = (1), (row 2) = (2), and (row 3) = (3). For n >= 4, row n consists of numbers in decreasing order generated as follows: x+1 for each x in row n-1 together with 2/x for each x in row n-1, and duplicates are rejected as they occur. Then a(n) = (number of numbers in row n); it appears that this sequence is not linearly recurrent.

Links

Table of n, a(n) for n=1..32.

Example

First 6 rows of the array of rationals:
1/1
2/1
3/1
4/1 ... 2/3
5/1 ... 5/3 ... 1/2
6/1 ... 8/3 ... 3/2 ... 6/5 ... 2/5, so that a begins with 1,1,1,2,3,5.

Mathematica

z = 12; g[1] = {1}; f1[x_] := x + 1; 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]]]
u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];
Denominator[v] (* A243848 *)
Numerator[v]   (* A243849 *)
Table[Length[g[n]], {n, 1, z}] (* A243850 *)

Crossrefs

Cf. A243848, A243849, A243853.

Sequence in context: A303668 A060961 A225393 * A357519 A179018 A352476

Adjacent sequences: A243847 A243848 A243849 * A243851 A243852 A243853

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2014

Status

approved