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 A288133 #12 Feb 18 2021 00:36:09
%S A288133 1,2,4,7,12,21,38,71,136,265,522,1035,2060,4109,8206,16399,32784,
%T A288133 65553,131090,262163,524308,1048597,2097174,4194327,8388632,16777241,
%U A288133 33554458,67108891,134217756,268435485
%N A288133 Positions of 0 in A288132; complement of A288134.
%C A288133 a(n+1)/a(n) -> 2. It appears that a(n) = A005126(n-2) for n >= 2.
%C A288133 This conjecture by Kimberling is proved in A288132. - _Michel Dekking_, Feb 18 2021
%F A288133 Conjectures from _Colin Barker_, Jun 09 2017: (Start)
%F A288133 G.f.: x*(1 - 2*x + x^2 - x^3) / ((1 - x)^2*(1 - 2*x)).
%F A288133 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>4.
%F A288133 (End)
%F A288133 Colin Barker's conjectures are a consequence of
%F A288133 a(n) = 2^{n-2} + n - 1 = A005126(n-2) for n >= 2. - _Michel Dekking_, Feb 18 2021
%t A288133 s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t A288133 w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "1" -> "11"}]
%t A288133 Table[w[n], {n, 0, 8}]
%t A288133 st = ToCharacterCode[w[11]] - 48 (* A288132 *)
%t A288133 Flatten[Position[st, 0]] (* A288133 *)
%t A288133 Flatten[Position[st, 1]] (* A288134 *)
%Y A288133 Cf. A288132, A288134.
%K A288133 nonn,easy
%O A288133 1,2
%A A288133 _Clark Kimberling_, Jun 07 2017