%I #8 Jul 04 2016 05:54:26
%S 1,1,1,1,1,2,2,3,3,5,6,8,9,13,17,22,27,36,47,61,77,101,132,171,219,
%T 285,370,480,619,803,1042,1351,1747,2264,2936,3805,4927,6385,8276,
%U 10725,13894,18004,23333,30238,39179,50770,65794,85261,110483,143171,185534,240432,311566,403749,523216,678031
%N Number of integers in n-th generation of tree T(2^(-1/3)) defined in Comments.
%C 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 n-th 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.
%C See A274142 for a guide to related sequences.
%H Kenny Lau, <a href="/A274158/b274158.txt">Table of n, a(n) for n = 0..8877</a>
%e If r = 2^(-1/3), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t u = Table[t[[k]] /. x -> 2^(-1/3), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y Cf. A274142.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Jun 12 2016
%E More terms from _Kenny Lau_, Jul 04 2016