%I #7 Jul 04 2016 20:00:48
%S 1,1,1,2,3,6,10,19,33,62,112,212,394,751,1419,2719,5193,10002,19254,
%T 37258,72132,140108,272368,530646,1034798,2021127,3951147,7733421,
%U 15148711,29702087,58279135,114438213,224856997,442099674,869717486,1711885120,3371215170,6642102554,13092289634,25817134600
%N Number of real integers in n-th generation of tree T(i) 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="/A274160/b274160.txt">Table of n, a(n) for n = 0..1455</a>
%e If r = i, then g(3) = {3,2r,r+1, r^2}, in which the number of real integers is a(3) = 2.
%t z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t u = Table[t[[k]] /. x -> I, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y Cf. A274142.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Jun 12 2016
%E More terms from _Kenny Lau_, Jul 05 2016