

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
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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 n1 together with 3/x for each x in row n1, 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



