%I #14 Jul 01 2017 03:00:22
%S 1,1,1,2,2,4,5,8,12,18,27,41,60,92,134,206,305,463,694,1041,1561,2344,
%T 3506,5279,7903,11877,17823,26689,40100,60041,90217,135312,202940,
%U 304555,456295,685209,1027291,1541669,2312510,3466919,5203662,7801283,11707295,17559032,26334864
%N Number of integers in n-th generation of tree T(-3/2) 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="/A274154/b274154.txt">Table of n, a(n) for n = 0..72</a>
%e For r = -3/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of 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 -> -3/2, {k, 1, z}]; Table[
%t 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_, Jun 30 2017