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 A266724 #23 Feb 16 2025 08:33:28
%S A266724 0,1,3,1,7,1,11,1,15,1,19,1,23,1,27,1,31,1,35,1,39,1,43,1,47,1,51,1,
%T A266724 55,1,59,1,63,1,67,1,71,1,75,1,79,1,83,1,87,1,91,1,95,1,99,1,103,1,
%U A266724 107,1,111,1,115,1,119,1,123,1,127,1,131,1,135,1,139,1
%N A266724 Number of OFF (white) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
%D A266724 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266724 Robert Price, <a href="/A266724/b266724.txt">Table of n, a(n) for n = 0..1000</a>
%H A266724 Paul Barry, <a href="https://arxiv.org/abs/2004.04577">On a Central Transform of Integer Sequences</a>, arXiv:2004.04577 [math.CO], 2020.
%H A266724 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266724 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A266724 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266724 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266724 Conjectures from _Colin Barker_, Jan 05 2016 and Apr 18 2019: (Start)
%F A266724 a(n) = (-1)^n*(n-1)+n for n>0.
%F A266724 a(n) = 2*a(n-2)-a(n-4) for n>4.
%F A266724 G.f.: x*(1+3*x-x^2+x^3) / ((1-x)^2*(1+x)^2).
%F A266724 (End)
%t A266724 rule=59; 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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y A266724 Cf. A266716.
%K A266724 nonn
%O A266724 0,3
%A A266724 _Robert Price_, Jan 03 2016