

A274144


Number of integers in nth generation of tree T(1/4) defined in Comments.


2



1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 5, 8, 8, 9, 12, 16, 17, 21, 27, 32, 37, 47, 57, 67, 82, 102, 121, 145, 180, 219, 260, 317, 391, 470, 564, 691, 843, 1012, 1225, 1500, 1816, 2188, 2663, 3245, 3918, 4744, 5778, 7010, 8473, 10291, 12511, 15148
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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..11916


EXAMPLE

For r = 1/4, we have g(3) = {3,2r,r+1, r^2}, in which only 3 is an integer, so that a(3) = 1.


MATHEMATICA

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


CROSSREFS

Cf. A274142.
Sequence in context: A029079 A035398 A104409 * A214628 A032576 A276420
Adjacent sequences: A274141 A274142 A274143 * A274145 A274146 A274147


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 11 2016


EXTENSIONS

More terms from Kenny Lau, Jul 01 2016


STATUS

approved



