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 A266180 #34 Feb 16 2025 08:33:28
%S A266180 1,6,16,96,256,1536,4096,24576,65536,393216,1048576,6291456,16777216,
%T A266180 100663296,268435456,1610612736,4294967296,25769803776,68719476736,
%U A266180 412316860416,1099511627776,6597069766656,17592186044416,105553116266496,281474976710656
%N A266180 Decimal representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell.
%C A266180 A001025 is a subsequence. - _Altug Alkan_, Dec 23 2015
%C A266180 Rules 38, 134 and 166 also generate this sequence.
%D A266180 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266180 Robert Price, <a href="/A266180/b266180.txt">Table of n, a(n) for n = 0..999</a>
%H A266180 Hans Montanus and Ron Westdijk, <a href="https://greenbluemath.nl/wp-content/uploads/2024/03/Cellular-Automation-and-Binomials.pdf">Cellular Automation and Binomials</a>, Green Blue Mathematics (2022), p. 22.
%H A266180 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266180 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266180 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266180 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,16).
%F A266180 From _Colin Barker_, Dec 23 2015 and Apr 13 2019: (Start)
%F A266180 a(n) = 4^(n-1)*(5-(-1)^n).
%F A266180 a(n) = 16*a(n-2) for n>1.
%F A266180 G.f.: (1+6*x) / ((1-4*x)*(1+4*x)).
%F A266180 (End)
%t A266180 rule=6; 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 *)
%t A266180 LinearRecurrence[{0,16},{1,6},30] (* _Harvey P. Dale_, May 25 2016 *)
%o A266180 (Python) print([int(4**(n-1)*(5-(-1)**n)) for n in range(30)]) # _Karl V. Keller, Jr._, Jun 03 2021
%Y A266180 Cf. A001025, A266178, A266179, A019590, A003953, A003945, A000034, A032766, A042948, A035608.
%K A266180 nonn,easy
%O A266180 0,2
%A A266180 _Robert Price_, Dec 22 2015