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 A267539 #45 Feb 16 2025 08:33:29
%S A267539 1,3,6,12,25,51,103,207,415,831,1663,3327,6655,13311,26623,53247,
%T A267539 106495,212991,425983,851967,1703935,3407871,6815743,13631487,
%U A267539 27262975,54525951,109051903,218103807,436207615,872415231,1744830463,3489660927,6979321855
%N A267539 Decimal representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.
%H A267539 Robert Price, <a href="/A267539/b267539.txt">Table of n, a(n) for n = 0..1000</a>
%H A267539 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267539 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A267539 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267539 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267539 Conjectures from _Colin Barker_, Jan 17 2016 and Apr 20 2019: (Start)
%F A267539 a(n) = 3*a(n-1)-2*a(n-2) for n > 4. [n range correction by _Karl V. Keller, Jr._, Apr 14 2022]
%F A267539 G.f.: (1-x^2+x^4) / ((1-x)*(1-2*x)).
%F A267539 (End)
%F A267539 {1,3,6} followed by A198274 (conjectured). - _Robert Price_, Jan 17 2016
%t A267539 rule=143; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* truncated list of each row *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* keep only middle cell from each row *) Table[FromDigits[Take[mc,k],2],{k,1,rows}] (* binary representation of middle column *)
%o A267539 (PARI) a(n) = bitneg(3<<(n-3),n+1); \\ _Kevin Ryde_, Apr 15 2022
%Y A267539 Cf. A267533, A267538.
%K A267539 nonn,easy
%O A267539 0,2
%A A267539 _Robert Price_, Jan 16 2016