A243853 Number of numbers in row n of the array at A243851.

1, 2, 2, 3, 5, 8, 12, 19, 30, 47, 75, 118, 187, 294, 465, 736, 1160, 1837, 2900, 4586, 7253, 11465, 18132, 28669, 45344, 71715, 113416, 179394, 283737, 448838, 709971, 1123055

Offset

1,2

Comments

Decree that (row 1) = (1) and (row 2) = (3,2). 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 3/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
3/1 ... 2/1
4/1 ... 3/2
5/1 ... 5/2 ... 3/4
6/1 ... 7/2 ... 7/4 ... 6/5 ... 3/5
7/1 ... 9/2 ... 11/4 .. 11/5 .. 12/7 .. 8/5 .. 6/7 .. 1/2, so that A242453 begins with 1,2,2,3,5,8.

Mathematica

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 3/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] (* A243851 *)
Numerator[v]   (* A243852 *)
Table[Length[g[n]], {n, 1, z}] (* A243853 *)

Crossrefs

Cf. A243851, A243852, A243850.

Sequence in context: A347546 A152948 A018136 * A293419 A277218 A293643

Adjacent sequences: A243850 A243851 A243852 * A243854 A243855 A243856

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2014

Status

approved