A228894 - OEIS

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, 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