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%I #8 Sep 09 2013 08:25:03
%S 1,3,4,5,6,9,11,13,14,16,17,19,22,23,27,28,31,32,33,35,37,38,39,40,43,
%T 45,47,48,51,52,53,55,57,59,60,62,63,65,67,70,71,73,75,78,79,80,83,84,
%U 85,86,87,88,92,95,97,101,102,103,106,107,113,115,118,119
%N Nodes of tree generated as follows: (3,1) 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).
%H Vincenzo Librandi, <a href="/A228895/b228895.txt">Table of n, a(n) for n = 1..1000</a>
%e Taking the first generation of edges to be G(1) = {(3,1)}, the edge (3,1) grows G(2) = {(1,4), (1,5)}, which grows G(3) = {(4,5), (4,9), (5,6), (5,11)}, ... Expelling duplicate nodes and sorting leave (1,2,4,5,6,9,11,...).
%t f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; 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. A228855.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 08 2013
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