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A228894 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. 1

%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

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Last modified November 18 17:45 EST 2019. Contains 329287 sequences. (Running on oeis4.)