

A274151


Number of integers in nth generation of tree T(3/4) defined in Comments.


2



1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 6, 8, 11, 14, 17, 20, 26, 36, 45, 56, 74, 96, 120, 150, 191, 245, 318, 405, 517, 665, 850, 1073, 1364, 1749, 2233, 2860, 3660, 4678, 5970, 7610, 9691, 12357, 15808, 20190, 25815, 32990, 42127, 53730, 68537, 87474, 111636, 142653, 182214, 232784, 297231, 379421
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OFFSET

0,6


COMMENTS

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the nth generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.
See A274142 for a guide to related sequences.


LINKS

Kenny Lau, Table of n, a(n) for n = 0..9418


EXAMPLE

For r = 3/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.


MATHEMATICA

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x > 3/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]


CROSSREFS

Cf. A274142.
Sequence in context: A078635 A286305 A046768 * A216393 A045812 A064877
Adjacent sequences: A274148 A274149 A274150 * A274152 A274153 A274154


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 11 2016


EXTENSIONS

More terms from Kenny Lau, Jul 02 2016


STATUS

approved



