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A274158 Number of integers in n-th generation of tree T(2^(-1/3)) defined in Comments.

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