This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274145 #20 Jul 04 2016 03:53:43
%S A274145 1,1,1,1,2,2,3,4,5,6,9,11,14,19,25,32,43,56,73,97,128,167,222,292,384,
%T A274145 507,670,882,1165,1539,2030,2680,3541,4675,6173,8155,10772,14227,
%U A274145 18798,24834,32808,43350,57279,75681,100006,132152,174627,230766,304963,403012,532600,703874,930227,1229386
%N A274145 Number of integers in n-th generation of tree T(2/3) defined in Comments.
%C A274145 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 A274145 See A274142 for a guide to related sequences.
%H A274145 Kenny Lau, <a href="/A274145/b274145.txt">Table of n, a(n) for n = 0..8248</a>
%e A274145 For r = 2/3, we have g(3) = {3,2r,r+1, r^2}, in which only 3 is an integer, so that a(3) = 1.
%t A274145 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274145 u = Table[t[[k]] /. x -> 2/3, {k, 1, z}];
%t A274145 Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274145 Cf. A274142.
%K A274145 nonn,easy
%O A274145 0,5
%A A274145 _Clark Kimberling_, Jun 11 2016
%E A274145 More terms from _Kenny Lau_, Jul 01 2016