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 A265380 #40 Feb 16 2025 08:33:27
%S A265380 1,11,111,1110,11101,111011,1110111,11101110,111011101,1110111011,
%T A265380 11101110111,111011101110,1110111011101,11101110111011,
%U A265380 111011101110111,1110111011101110,11101110111011101,111011101110111011,1110111011101110111,11101110111011101110
%N A265380 Binary representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.
%D A265380 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A265380 Robert Price, <a href="/A265380/b265380.txt">Table of n, a(n) for n = 0..999</a>
%H A265380 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A265380 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A265380 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A265380 Conjectures from _Colin Barker_, Dec 14 2015 and Apr 18 2019: (Start)
%F A265380 a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5) for n>4.
%F A265380 G.f.: (1+x+x^2) / ((1-x)*(1+x)*(1-10*x)*(1+x^2)).
%F A265380 (End)
%e A265380 From _Michael De Vlieger_, Dec 09 2015: (Start)
%e A265380 First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row :
%e A265380 (1) -> 1
%e A265380 1 (1) 1 -> 11
%e A265380 1 1 (1) 0 1 -> 111
%e A265380 1 1 1 (0) 0 1 1 -> 1110
%e A265380 1 1 1 0 (1) 1 1 0 1 -> 11101
%e A265380 1 1 1 0 0 (1) 1 0 0 1 1 -> 111011
%e A265380 1 1 1 0 1 1 (1) 0 1 1 1 0 1 -> 1110111
%e A265380 1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 -> 11101110
%e A265380 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 -> 111011101
%e A265380 1 1 1 0 0 1 1 0 0 (1) 1 0 0 1 1 0 0 1 1 -> 1110111011
%e A265380 1 1 1 0 1 1 1 0 1 1 (1) 0 1 1 1 0 1 1 1 0 1 -> 11101110111
%e A265380 1 1 1 0 0 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 0 0 1 1 -> 111011101110
%e A265380 1 1 1 0 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 1 1 0 1 -> 1110111011101
%e A265380 (End)
%t A265380 f[n_] := Block[{w = {}}, Do[AppendTo[w, Boole[Mod[k, 4] != 3]], {k, 0, n}]; FromDigits@ w]; Table[f@ n, {n, 0, 19}] (* _Michael De Vlieger_, Dec 09 2015 *)
%Y A265380 Cf. A071037, A265381.
%K A265380 nonn,easy
%O A265380 0,2
%A A265380 _Robert Price_, Dec 07 2015
%E A265380 Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed 2 programs based on conjectures. - _N. J. A. Sloane_, Jun 13 2022