

A228894


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


1



1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 35, 37, 40, 41, 43, 44, 47, 48, 51, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 69, 71, 75, 76, 78, 79, 80, 83, 84, 85, 87, 88, 89, 91, 92, 93, 97, 98, 99
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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). For example, the branch 2>1>3>4>7>11> contributes the Lucas sequence, A000032. The other extreme branch, 1>4>9>22>53> contributes A048654.


LINKS

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


EXAMPLE

Taking the first generation of edges to be G(1) = {(2,1)}, the edge (2,1) grows G(2) = {(1,3), (1,4)}, which grows G(3) = {(3,4), (3,7), (4,5), (4,9)}, ... Expelling duplicate nodes and sorting leave (1,2,3,4,5,7,9,...).


MATHEMATICA

f[x_, y_] := {{y, x + y}, {y, x + 2 y}}; x = 2; 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. A228853.
Sequence in context: A088962 A047363 A191917 * A325367 A160718 A122090
Adjacent sequences: A228891 A228892 A228893 * A228895 A228896 A228897


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Sep 08 2013


STATUS

approved



