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Number of real integers in n-th generation of tree T(i) defined in Comments.
7

%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