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

%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