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 A267458 #24 Feb 16 2025 08:33:29
%S A267458 1,1,1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21,21,23,23,25,
%T A267458 25,27,27,29,29,31,31,33,33,35,35,37,37,39,39,41,41,43,43,45,45,47,47,
%U A267458 49,49,51,51,53,53,55,55,57,57,59,59,61,61,63,63,65,65
%N A267458 Number of ON (black) cells in the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
%C A267458 1,1, followed by A109613 (odd integers repeated).
%D A267458 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267458 Robert Price, <a href="/A267458/b267458.txt">Table of n, a(n) for n = 0..1000</a>
%H A267458 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267458 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267458 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267458 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267458 a(n) = A109613(n-2) for n>=2.
%F A267458 Conjectures from _Colin Barker_, Jan 15 2016 and Apr 19 2019: (Start)
%F A267458 a(n) = (2*n+(-1)^n-3)/2 for n>1.
%F A267458 a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.
%F A267458 G.f.: (1-x^2+2*x^4) / ((1-x)^2*(1+x)).
%F A267458 (End)
%t A267458 rule=133; 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[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)
%Y A267458 Cf. A267423.
%K A267458 nonn,easy
%O A267458 0,5
%A A267458 _Robert Price_, Jan 15 2016