%I
%S 1,2,3,4,5,7,9,10,11,13,14,15,17,18,19,22,23,24,25,26,27,29,31,32,33,
%T 35,37,40,41,43,44,47,48,51,52,53,55,56,57,58,60,61,63,64,65,67,68,69,
%U 71,75,76,78,79,80,83,84,85,87,88,89,91,92,93,97,98,99
%N Nodes of tree generated as follows: (2,1) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.
%C The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not). For example, the branch 2>1>3>4>7>11> contributes the Lucas sequence, A000032. The other extreme branch, 1>4>9>22>53> contributes A048654.
%H Vincenzo Librandi, <a href="/A228894/b228894.txt">Table of n, a(n) for n = 1..1000</a>
%e Taking the first generation of edges to be G(1) = {(2,1)}, the edge (2,1) grows G(2) = {(1,3), (1,4)}, which grows G(3) = {(3,4), (3,7), (4,5), (4,9)}, ... Expelling duplicate nodes and sorting leave (1,2,3,4,5,7,9,...).
%t f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; y = 1; t = {{x, y}};
%t u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u];
%t w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
%t Sort[Union[w]]
%Y Cf. A228853.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 08 2013
