cp's OEIS Frontend

A274148 Number of integers in n-th generation of tree T(-1/3) defined in Comments.

%I A274148 #18 Jul 02 2016 01:24:42
%S A274148 1,1,1,1,2,2,3,5,6,8,12,17,23,32,44,61,86,119,164,228,318,442,614,850,
%T A274148 1181,1643,2282,3167,4398,6110,8489,11790,16372,22737,31584,43870,
%U A274148 60930,84622,117533,163248,226742,314918,437389,607498,843772,1171927,1627699
%N A274148 Number of integers in n-th generation of tree T(-1/3) defined in Comments.
%C A274148 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 A274148 See A274142 for a guide to related sequences.
%H A274148 Kenny Lau, <a href="/A274148/b274148.txt">Table of n, a(n) for n = 0..7004</a>
%e A274148 For r = -1/3, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274148 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274148 u = Table[t[[k]] /. x -> -1/3, {k, 1, z}];
%t A274148 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274148 Cf. A274142.
%K A274148 nonn,easy
%O A274148 0,5
%A A274148 _Clark Kimberling_, Jun 11 2016
%E A274148 More terms from _Kenny Lau_, Jul 01 2016