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, 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

Offset: 1

Author

Clark Kimberling, Sep 08 2013

Keywords

• nonn
• easy

Comments

The tree has infinitely many branches which are essentially linear recurrence sequences (and infinitely many which are not).

Examples

			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,...).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A228855.

Programs

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]]