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 A228895 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. 1
 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, 45, 47, 48, 51, 52, 53, 55, 57, 59, 60, 62, 63, 65, 67, 70, 71, 73, 75, 78, 79, 80, 83, 84, 85, 86, 87, 88, 92, 95, 97, 101, 102, 103, 106, 107, 113, 115, 118, 119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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) = {(3,1)}, 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,...). MATHEMATICA f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 1; 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. A228855. Sequence in context: A104373 A047427 A228235 * A267322 A218929 A088875 Adjacent sequences:  A228892 A228893 A228894 * A228896 A228897 A228898 KEYWORD nonn,easy AUTHOR Clark Kimberling, Sep 08 2013 STATUS approved

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Last modified January 18 14:01 EST 2020. Contains 331010 sequences. (Running on oeis4.)