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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)