cp's OEIS Frontend

A274149 Number of integers in n-th generation of tree T(-1/4) defined in Comments.

%I A274149 #22 Jul 02 2016 01:24:52
%S A274149 1,1,1,1,1,2,2,3,4,6,7,9,12,17,22,29,38,51,68,90,119,158,209,277,368,
%T A274149 489,648,858,1137,1509,2002,2655,3520,4667,6189,8208,10885,14436,
%U A274149 19141,25382,33659,44638,59195,78497,104092,138036,183050,242745,321904,426875
%N A274149 Number of integers in n-th generation of tree T(-1/4) defined in Comments.
%C A274149 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 A274149 See A274142 for a guide to related sequences.
%H A274149 Kenny Lau, <a href="/A274149/b274149.txt">Table of n, a(n) for n = 0..8153</a>
%F A274149 a(n-1) = length of row n of the array in A274185.
%e A274149 For r = -1/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.
%t A274149 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274149 u = Table[t[[k]] /. x -> -1/4, {k, 1, z}];
%t A274149 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274149 Cf. A274142.
%K A274149 nonn,easy
%O A274149 0,6
%A A274149 _Clark Kimberling_, Jun 11 2016
%E A274149 More terms from _Kenny Lau_, Jul 01 2016