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 A266975 #24 Feb 16 2025 08:33:29
%S A266975 1,110,11100,1101000,111010000,11010100000,1110101000000,
%T A266975 110101010000000,11101010100000000,1101010101000000000,
%U A266975 111010101010000000000,11010101010100000000000,1110101010101000000000000,110101010101010000000000000,11101010101010100000000000000
%N A266975 Binary representation of the n-th iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell.
%H A266975 Robert Price, <a href="/A266975/b266975.txt">Table of n, a(n) for n = 0..1000</a>
%H A266975 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266975 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266975 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266975 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266975 Conjectures from _Colin Barker_, Jan 08 2016 and Apr 18 2019: (Start)
%F A266975 a(n) = 2^(n-2)*5^(n-1)*(9*(-10)^n+2189*10^n-20)/99 for n>0.
%F A266975 a(n) = 10*a(n-1)+10000*a(n-2)-100000*a(n-3) for n>3.
%F A266975 G.f.: (1+100*x-10000*x^3) / ((1-10*x)*(1-100*x)*(1+100*x)).
%F A266975 (End)
%t A266975 rule=78; 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]]],{k,1,rows}] (* Binary Representation of Rows *)
%Y A266975 Cf. A266974, A266976.
%K A266975 nonn,easy
%O A266975 0,2
%A A266975 _Robert Price_, Jan 07 2016