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 A293078 #8 Oct 02 2017 07:58:16
%S A293078 1,2,3,5,8,13,22,37,63,107,182,310,529,903,1541,2630,4489,7663,13081,
%T A293078 22330,38119,65073,111086,189635,323727,552636,943408,1610498,2749292,
%U A293078 4693335,8012024,13677380,23348748,39858806,68043238
%N A293078 a(n) = (1/2)*A293077(n).
%t A293078 z = 10; (* number of iterations *)
%t A293078 s = {0, 0}; u[0] = StringJoin[Map[ToString, s]]; w[0] = u[0];
%t A293078 u[n_] := u[n] = StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "010"}];
%t A293078 w[n_] := w[n] = If[OddQ[StringLength[u[n]]], StringDrop[u[n], -1], u[n]];
%t A293078 TableForm[Table[w[n], {n, 0, 8}]]
%t A293078 st = ToCharacterCode[w[z]] - 48 (* A293076 *)
%t A293078 p0 = Flatten[Position[st, 0]] (* A289036 *)
%t A293078 p1 = Flatten[Position[st, 1]] (* A289037 *)
%t A293078 v = Table[StringLength[w[n]], {n, 0, 34}] (* A293077 *)
%t A293078 v/2 (* A293078 *)
%Y A293078 Cf. A289035, A293076, A293077.
%K A293078 nonn,easy
%O A293078 1,2
%A A293078 _Clark Kimberling_, Sep 30 2017