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

Author

Clark Kimberling, Jun 12 2014

Keywords

• nonn
• easy

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.

Examples

			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.
		

Crossrefs

Cf. A243848, A243849, A243853.

Programs

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 *)