

A228896


Nodes of tree generated as follows: (3,2) is an edge, and if (x,y) is an edge, then (y,y+x) and (y,2y+x) are edges.


1



2, 3, 5, 7, 9, 12, 16, 17, 19, 23, 25, 26, 29, 31, 34, 39, 41, 43, 45, 46, 50, 55, 57, 59, 62, 63, 64, 66, 69, 70, 71, 74, 75, 81, 84, 85, 91, 93, 94, 97, 98, 99, 101, 104, 105, 107, 109, 111, 112, 116, 117, 119, 121, 127, 131, 133, 139, 140, 143, 147, 148
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OFFSET

1,1


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) = {(3,2)}, the edge (3,2) grows G(2) = {(2,5), (2,7)}, which grows G(3) = {(5,7), (5,12), (7,9), (7,16)}, ... Expelling duplicate nodes and sorting leave (2,3,5,7,9,12,...).


MATHEMATICA

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 3; y = 2; 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

Cf. A228856.
Sequence in context: A293230 A133231 A235111 * A281783 A224854 A074752
Adjacent sequences: A228893 A228894 A228895 * A228897 A228898 A228899


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Sep 08 2013


STATUS

approved



