A228940 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y, y^2 - x^2) and (y, y^2 + x^2) are edges.

1, 2, 3, 5, 13, 16, 21, 29, 34, 160, 178, 231, 281, 416, 466, 816, 866, 1131, 1181, 25431, 25769, 31515, 31853, 53105, 53617, 78705, 79217, 172615, 173497, 216715, 217597, 665015, 666697, 749115, 750797, 1278005, 1280317, 1393605, 1395917, 646710161

Offset: 1

Author

Clark Kimberling, Sep 08 2013

Keywords

• nonn
• easy

Examples

			Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5)}, which grows G(3) = {(3,5), (3,14), (5,21), (5,29)}, ... Expelling duplicate nodes and sorting leave (1, 2, 3, 5, 13, 16, 21, 29, 34, 160,...).
		

Links

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

Crossrefs

Cf. A228853, A228940.

Programs

Mathematica

f[x_, y_] := {{y, y^2-x^2}, {y, y^2 + x^2}}; x = 1; y = 2; t = {{x, y}};
u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {15}]; v = Flatten[u];
w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];
Sort[Union[w]]