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A274156 Number of integers in n-th generation of tree T(2^(-1/2)) defined in Comments.

%I A274156 #14 Jul 02 2016 01:25:09
%S A274156 1,1,1,1,2,2,3,4,6,7,10,14,19,25,35,47,64,87,119,161,220,300,407,554,
%T A274156 757,1028,1399,1908,2598,3534,4816,6560,8929,12161,16567,22556,30718,
%U A274156 41843,56981,77597,105693,143944,196029,266991,363634,495228,674481,918629,1251106,1703941,2320726,3160713,4304733
%N A274156 Number of integers in n-th generation of tree T(2^(-1/2)) defined in Comments.
%C A274156 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 A274156 See A274142 for a guide to related sequences.
%H A274156 Kenny Lau, <a href="/A274156/b274156.txt">Table of n, a(n) for n = 0..7448</a>
%e A274156 If r = 2^(-1/2), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274156 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274156 u = Table[t[[k]] /. x -> 2^(-1/2), {k, 1, z}];
%t A274156 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274156 Cf. A274142.
%K A274156 nonn,easy
%O A274156 0,5
%A A274156 _Clark Kimberling_, Jun 12 2016
%E A274156 More terms from _Kenny Lau_, Jul 01 2016