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

1,2

Links

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

Example

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,...).

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]]

Crossrefs

Cf. A228853, A228940.

Sequence in context: A058592 A268509 A260594 * A045311 A356196 A045312

Adjacent sequences: A228937 A228938 A228939 * A228941 A228942 A228943

Keyword

nonn,easy

Author

Clark Kimberling, Sep 08 2013

Status

approved