cp's OEIS Frontend

A274150 Number of integers in n-th generation of tree T(-2/3) defined in Comments.

%I A274150 #16 Jul 02 2016 01:24:58
%S A274150 1,1,1,1,2,2,2,4,5,7,10,14,17,23,33,43,61,82,111,150,202,278,376,516,
%T A274150 694,941,1281,1731,2369,3208,4364,5915,8015,10911,14792,20139,27314,
%U A274150 37082,50358,68309,92891,126054,171277,232504,315584,428704,581880,790589,1073298,1457466,1979119,2686767,3649316
%N A274150 Number of integers in n-th generation of tree T(-2/3) defined in Comments.
%C A274150 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 A274150 See A274142 for a guide to related sequences.
%H A274150 Kenny Lau, <a href="/A274150/b274150.txt">Table of n, a(n) for n = 0..7521</a>
%e A274150 For r = -2/3, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274150 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274150 u = Table[t[[k]] /. x -> -2/3, {k, 1, z}];
%t A274150 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274150 Cf. A274142.
%K A274150 nonn,easy
%O A274150 0,5
%A A274150 _Clark Kimberling_, Jun 11 2016
%E A274150 More terms from _Kenny Lau_, Jul 01 2016