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 A274168 #12 Nov 18 2024 22:31:19
%S A274168 1,1,1,1,1,1,2,2,3,3,5,5,7,9,13,18,25,33,43
%N A274168 Number of real integers in n-th generation of tree T(r) defined in Comments, where r^2 = -r - 1 (i.e., r = (-1 + sqrt(3))/2).
%C A274168 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 A274168 See A274142 for a guide to related sequences.
%e A274168 If r = (-1 + sqrt(3))/2, then g(3) = {3,2r,r+1,r^2}, in which the number of real integers is a(3) = 1.
%t A274168 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274168 u = Table[t[[k]] /. x -> (-1 + 3 I)/2, {k, 1, z}]; Table[
%t A274168 Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274168 Cf. A274142.
%K A274168 nonn,more
%O A274168 0,7
%A A274168 _Clark Kimberling_, Jun 13 2016