A228894 Nodes of tree generated as follows: (2,1) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.

1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 35, 37, 40, 41, 43, 44, 47, 48, 51, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 69, 71, 75, 76, 78, 79, 80, 83, 84, 85, 87, 88, 89, 91, 92, 93, 97, 98, 99

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). For example, the branch 2->1->3->4->7->11-> contributes the Lucas sequence, A000032. The other extreme branch, 1->4->9->22->53-> contributes A048654.

Examples

			Taking the first generation of edges to be G(1) = {(2,1)}, the edge (2,1) grows G(2) = {(1,3), (1,4)}, which grows G(3) = {(3,4), (3,7), (4,5), (4,9)}, ... Expelling duplicate nodes and sorting leave (1,2,3,4,5,7,9,...).
		

Links

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

Crossrefs

Cf. A228853.

Programs

Mathematica

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; 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]]