A243853 - OEIS

%I #8 Aug 13 2014 18:21:14

%S 1,2,2,3,5,8,12,19,30,47,75,118,187,294,465,736,1160,1837,2900,4586,

%T 7253,11465,18132,28669,45344,71715,113416,179394,283737,448838,

%U 709971,1123055

%N Number of numbers in row n of the array at A243851.

%C 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.

%e First 6 rows of the array of rationals:

%e 1/1

%e 3/1 ... 2/1

%e 4/1 ... 3/2

%e 5/1 ... 5/2 ... 3/4

%e 6/1 ... 7/2 ... 7/4 ... 6/5 ... 3/5

%e 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.

%t z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 3/x; h[1] = g[1];

%t b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];

%t h[n_] := h[n] = Union[h[n - 1], g[n - 1]];

%t g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]

%t u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];

%t Denominator[v] (* A243851 *)

%t Numerator[v]   (* A243852 *)

%t Table[Length[g[n]], {n, 1, z}] (* A243853 *)

%Y Cf. A243851, A243852, A243850.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 12 2014