cp's OEIS Frontend

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

%I A243856 #10 Aug 13 2014 18:21:34
%S A243856 1,2,2,3,4,7,11,17,27,44,70,111,176,281,447,712,1130,1797,2856,4549,
%T A243856 7233,11517,18317,29163,46389,73838,117503,187047,297690,473909,
%U A243856 754298,1200808
%N A243856 Number of numbers in row n of the array at A243855.
%C A243856 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 A243856 First 6 rows of the array of rationals:
%e A243856 1/1
%e A243856 4/1 ... 2/1
%e A243856 5/1 ... 3/1
%e A243856 6/1 ... 4/3 ... 4/5
%e A243856 7/1 ... 7/3 ... 9/5 ... 2/3
%e A243856 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.
%t A243856 z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4/x; h[1] = g[1];
%t A243856 b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];
%t A243856 h[n_] := h[n] = Union[h[n - 1], g[n - 1]];
%t A243856 g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]
%t A243856 u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];
%t A243856 Denominator[v] (* A243854 *)
%t A243856 Numerator[v]   (* A243855 *)
%t A243856 Table[Length[g[n]], {n, 1, z}] (* A243856 *)
%Y A243856 Cf. A243850, A243853.
%K A243856 nonn,easy
%O A243856 1,2
%A A243856 _Clark Kimberling_, Jun 12 2014