cp's OEIS Frontend

A243850 Number of numbers in row n of the array at A243848.

%I A243850 #10 Aug 19 2014 16:52:47
%S A243850 1,1,1,2,3,5,8,12,19,30,47,74,117,184,291,455,719,1135,1789,2821,4456,
%T A243850 7025,11097,17510,27645,43668,68973,108897,172051,271835,429442,678573
%N A243850 Number of numbers in row n of the array at A243848.
%C A243850 Decree that (row 1) = (1), (row 2) = (2), and (row 3) = (3).  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 2/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 A243850 First 6 rows of the array of rationals:
%e A243850 1/1
%e A243850 2/1
%e A243850 3/1
%e A243850 4/1 ... 2/3
%e A243850 5/1 ... 5/3 ... 1/2
%e A243850 6/1 ... 8/3 ... 3/2 ... 6/5 ... 2/5, so that a begins with 1,1,1,2,3,5.
%t A243850 z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 2/x; h[1] = g[1];
%t A243850 b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];
%t A243850 h[n_] := h[n] = Union[h[n - 1], g[n - 1]];
%t A243850 g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]
%t A243850 u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];
%t A243850 Denominator[v] (* A243848 *)
%t A243850 Numerator[v]   (* A243849 *)
%t A243850 Table[Length[g[n]], {n, 1, z}] (* A243850 *)
%Y A243850 Cf. A243848, A243849, A243853.
%K A243850 nonn,easy
%O A243850 1,4
%A A243850 _Clark Kimberling_, Jun 12 2014