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A243853 Number of numbers in row n of the array at A243851. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A039890 A152948 A018136 * A293419 A277218 A293643

Adjacent sequences:  A243850 A243851 A243852 * A243854 A243855 A243856

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)