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 A266753 #49 Feb 16 2025 08:33:28
%S A266753 1,4,18,74,298,1194,4778,19114,76458,305834,1223338,4893354,19573418,
%T A266753 78293674,313174698,1252698794,5010795178,20043180714,80172722858,
%U A266753 320690891434,1282763565738,5131054262954,20524217051818,82096868207274,328387472829098
%N A266753 Decimal representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell.
%D A266753 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266753 Robert Price, <a href="/A266753/b266753.txt">Table of n, a(n) for n = 0..1000</a>
%H A266753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266753 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A266753 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266753 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266753 Conjectures from _Colin Barker_, Jan 20 2016 and Apr 20 2019: (Start)
%F A266753 a(n) = 5*a(n-1)-4*a(n-2) for n>2.
%F A266753 G.f.: (1-x+2*x^2) / ((1-x)*(1-4*x)).
%F A266753 (End)
%F A266753 Empirical a(n) = (7*4^n - 4)/6 for n>1. - _Colin Barker_, Nov 25 2016 and Apr 20 2019
%F A266753 a(n) = 4*a(n-1) + 2, n>1, conjectured. - _Yosu Yurramendi_, Jan 22 2017
%F A266753 a(n) = 2*A020988(n) - A020988(n-1) = A020988(n) + 2^(2n-1) for n > 0, conjectured. - _Yosu Yurramendi_, Jan 24 2017 [n range correction - _Karl V. Keller, Jr._, May 07 2022]
%F A266753 a(n) = A072197(n-1) + A002450(n), n > 0, conjectured. - _Yosu Yurramendi_, Mar 03 2017
%t A266753 rule=163; 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 *) Table[FromDigits[catri[[k]],2],{k,1,rows}] (* Decimal Representation of Rows *)
%Y A266753 Cf. A263919, A266752.
%K A266753 nonn,easy
%O A266753 0,2
%A A266753 _Robert Price_, Jan 17 2016
%E A266753 Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _N. J. A. Sloane_, Jun 13 2022