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A274157 Number of integers in n-th generation of tree T(3^(-1/2)) defined in Comments.

%I A274157 #8 Jul 04 2016 05:53:54
%S A274157 1,1,1,1,1,2,2,2,3,4,4,6,7,9,11,14,16,22,26,33,40,53,62,82,97,127,151,
%T A274157 198,234,309,366,480,570,749,887,1165,1382,1815,2153,2827,3353,4405,
%U A274157 5224,6859,8137,10687,12675,16646,19746,25932,30761,40395,47917,62929,74647,98027,116285,152711,181150
%N A274157 Number of integers in n-th generation of tree T(3^(-1/2)) defined in Comments.
%C A274157 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 A274157 See A274142 for a guide to related sequences.
%H A274157 Kenny Lau, <a href="/A274157/b274157.txt">Table of n, a(n) for n = 0..10382</a>
%e A274157 If r = 3^(-1/2), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274157 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274157 u = Table[t[[k]] /. x -> 3^(-1/2), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274157 Cf. A274142.
%K A274157 nonn,easy
%O A274157 0,6
%A A274157 _Clark Kimberling_, Jun 12 2016
%E A274157 More terms from _Kenny Lau_, Jul 04 2016