cp's OEIS Frontend

A274151 Number of integers in n-th generation of tree T(-3/4) defined in Comments.

%I A274151 #13 Jul 04 2016 03:49:01
%S A274151 1,1,1,1,1,2,2,2,2,4,5,6,8,11,14,17,20,26,36,45,56,74,96,120,150,191,
%T A274151 245,318,405,517,665,850,1073,1364,1749,2233,2860,3660,4678,5970,7610,
%U A274151 9691,12357,15808,20190,25815,32990,42127,53730,68537,87474,111636,142653,182214,232784,297231,379421
%N A274151 Number of integers in n-th generation of tree T(-3/4) defined in Comments.
%C A274151 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 A274151 See A274142 for a guide to related sequences.
%H A274151 Kenny Lau, <a href="/A274151/b274151.txt">Table of n, a(n) for n = 0..9418</a>
%e A274151 For r = -3/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274151 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274151 u = Table[t[[k]] /. x -> -3/4, {k, 1, z}];
%t A274151 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274151 Cf. A274142.
%K A274151 nonn,easy
%O A274151 0,6
%A A274151 _Clark Kimberling_, Jun 11 2016
%E A274151 More terms from _Kenny Lau_, Jul 02 2016