A243856 Number of numbers in row n of the array at A243855.

1, 2, 2, 3, 4, 7, 11, 17, 27, 44, 70, 111, 176, 281, 447, 712, 1130, 1797, 2856, 4549, 7233, 11517, 18317, 29163, 46389, 73838, 117503, 187047, 297690, 473909, 754298, 1200808

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
4/1 ... 2/1
5/1 ... 3/1
6/1 ... 4/3 ... 4/5
7/1 ... 7/3 ... 9/5 ... 2/3
8/1 ... 10/3 ... 14/5 .. 20/9 .. 12/7 .. 5/3 .. 4/7, so that A243856 begins with 1,2,2,3,4,7.

Mathematica

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4/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] (* A243854 *)
Numerator[v]   (* A243855 *)
Table[Length[g[n]], {n, 1, z}] (* A243856 *)

Crossrefs

Cf. A243850, A243853.

Sequence in context: A245620 A059348 A110871 * A173433 A053638 A051920

Adjacent sequences: A243853 A243854 A243855 * A243857 A243858 A243859

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2014

Status

approved