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 A228896 Nodes of tree generated as follows: (3,2) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges. 1
 2, 3, 5, 7, 9, 12, 16, 17, 19, 23, 25, 26, 29, 31, 34, 39, 41, 43, 45, 46, 50, 55, 57, 59, 62, 63, 64, 66, 69, 70, 71, 74, 75, 81, 84, 85, 91, 93, 94, 97, 98, 99, 101, 104, 105, 107, 109, 111, 112, 116, 117, 119, 121, 127, 131, 133, 139, 140, 143, 147, 148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 EXAMPLE Taking the first generation of edges to be G(1) = {(3,2)}, the edge (3,2) grows G(2) = {(2,5), (2,7)}, which grows G(3) = {(5,7), (5,12), (7,9), (7,16)}, ... Expelling duplicate nodes and sorting leave (2,3,5,7,9,12,...). MATHEMATICA f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 2; t = {{x, y}}; u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {12}]; v = Flatten[u]; w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]]; Sort[Union[w]] CROSSREFS Cf. A228856. Sequence in context: A293230 A133231 A235111 * A281783 A224854 A074752 Adjacent sequences:  A228893 A228894 A228895 * A228897 A228898 A228899 KEYWORD nonn,easy AUTHOR Clark Kimberling, Sep 08 2013 STATUS approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)