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 A265427 #31 Feb 16 2025 08:33:27 %S A265427 1,11,101,1111,11101,110111,1011101,11110111,111011101,1101110111, %T A265427 10111011101,111101110111,1110111011101,11011101110111, %U A265427 101110111011101,1111011101110111,11101110111011101,110111011101110111,1011101110111011101,11110111011101110111 %N A265427 Binary representation of the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell. %D A265427 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. %H A265427 Robert Price, <a href="/A265427/b265427.txt">Table of n, a(n) for n = 0..999</a> %H A265427 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule188.html">Rule 188</a> %H A265427 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a> %H A265427 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %H A265427 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a> %F A265427 Conjectures from _Colin Barker_, Dec 09 2015 and Apr 18 2019: (Start) %F A265427 a(n) = a(n-2) + 10000*a(n-4) - 10000*a(n-6) for n>5. %F A265427 G.f.: (1+11*x+100*x^2+1100*x^3+1000*x^4-1000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1+100*x^2)). %F A265427 (End) %F A265427 Conjecture: a(n) = floor(11100*100^n/9999) + 10^n - floor(11100*10^n/9999)*10^n. - _Karl V. Keller, Jr._, Dec 15 2021 %e A265427 From _Michael De Vlieger_, Dec 09 2015: (Start) %e A265427 First 12 rows: %e A265427 1 %e A265427 1 1 %e A265427 1 0 1 %e A265427 1 1 1 1 %e A265427 1 1 1 0 1 %e A265427 1 1 0 1 1 1 %e A265427 1 0 1 1 1 0 1 %e A265427 1 1 1 1 0 1 1 1 %e A265427 1 1 1 0 1 1 1 0 1 %e A265427 1 1 0 1 1 1 0 1 1 1 %e A265427 1 0 1 1 1 0 1 1 1 0 1 %e A265427 1 1 1 1 0 1 1 1 0 1 1 1 %e A265427 1 1 1 0 1 1 1 0 1 1 1 0 1 %e A265427 (End) %t A265427 rule = 188; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}] %Y A265427 Cf. A118173, A118174. %K A265427 nonn,easy %O A265427 0,2 %A A265427 _Robert Price_, Dec 08 2015