

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



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
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OFFSET

1,2


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) = {(3,1)}, 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,...).


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]]


CROSSREFS

Cf. A228855.
Sequence in context: A104373 A047427 A228235 * A267322 A218929 A088875
Adjacent sequences: A228892 A228893 A228894 * A228896 A228897 A228898


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Sep 08 2013


STATUS

approved



