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