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 A267816 #21 Feb 16 2025 08:33:29
%S A267816 1,3,23,111,479,1983,8063,32511,130559,523263,2095103,8384511,
%T A267816 33546239,134201343,536838143,2147418111,8589803519,34359476223,
%U A267816 137438429183,549754765311,2199021158399,8796088827903,35184363700223,140737471578111,562949919866879
%N A267816 Decimal representation of the n-th iteration of the "Rule 221" elementary cellular automaton starting with a single ON (black) cell.
%D A267816 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267816 Robert Price, <a href="/A267816/b267816.txt">Table of n, a(n) for n = 0..1000</a>
%H A267816 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267816 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267816 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267816 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267816 Conjectures from _Colin Barker_, Jan 22 2016 and Apr 16 2019: (Start)
%F A267816 a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.
%F A267816 G.f.: (1-4*x+16*x^2-16*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
%F A267816 (End)
%F A267816 a(n) = 2^(n + 1) * (2^n - 1) - 1, for n > 0. - _Jaroslav Krizek_, Jan 22 2017
%t A267816 rule=221; 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 A267816 Cf. A267814.
%Y A267816 Similar entries: A085601 (2^(n + 1) * (2^n + 1) + 1), A092431 (2^(n - 1) * (2^n + 1) - 1), A092440 (2^(n + 1) * (2^n - 1) + 1), A129868 (2^(n - 1) * (2^n - 1) - 1), A134169 (2^(n - 1) * (2^n - 1) + 1), A281481 (2^(n - 1) * (2^n + 1) + 1), A281482 (2^(n + 1) * (2^n + 1) - 1). - _Jaroslav Krizek_, Jan 22 2017
%K A267816 nonn,easy
%O A267816 0,2
%A A267816 _Robert Price_, Jan 20 2016