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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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 08 2013
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)