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A228898 Nodes of tree generated as follows: (1,2) is an edge, and if (x,y) is an edge, then (y,x+y) and (y,x^2 + y^2) are edges. 1
1, 2, 3, 5, 7, 8, 12, 13, 16, 19, 21, 29, 31, 34, 39, 45, 50, 55, 63, 73, 74, 81, 89, 97, 112, 119, 131, 144, 155, 160, 178, 185, 186, 191, 193, 205, 212, 233, 236, 246, 257, 283, 297, 312, 343, 369, 377, 391, 398, 417, 425, 441, 469, 479, 482, 505, 524, 555 (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).  The extreme branches are (1,2)->(2,3)->(3,5)->(5,8)->... and (1,2)->(2,5)->(5,29)->(29,866)->...  These branches contribute to A228898, as subsequences, the Fibonacci numbers, A000045, and A000283.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Taking the first generation of edges to be G(1) = {(1,2)}, the edge (1,2) grows G(2) = {(2,3), (2,5)}, which grows G(3) = {(3,5), (3,13), (5,7), (5,29)}, ... Expelling duplicate nodes and sorting leave (1, 2, 3, 5, 7, 8, 12, 13, 16, 19,...).

MATHEMATICA

f[x_, y_] := {{y, x + y}, {y, x^2 + y^2}}; x = 1; y = 2; t = {{x, y}};

u = Table[t = Flatten[Map[Apply[f, #] &, t], 1], {18}]; v = Flatten[u];

w = Flatten[Prepend[Table[v[[2 k]], {k, 1, Length[v]/2}], {x, y}]];

Sort[Union[w]]

CROSSREFS

Cf. A228853, A000045.

Sequence in context: A090704 A112055 A291485 * A076386 A177801 A073301

Adjacent sequences:  A228895 A228896 A228897 * A228899 A228900 A228901

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 08 2013

STATUS

approved

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Last modified October 14 00:32 EDT 2019. Contains 327991 sequences. (Running on oeis4.)