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 A266218 #22 Feb 16 2025 08:33:28
%S A266218 1,6,0,127,0,2047,0,32767,0,524287,0,8388607,0,134217727,0,2147483647,
%T A266218 0,34359738367,0,549755813887,0,8796093022207,0,140737488355327,0,
%U A266218 2251799813685247,0,36028797018963967,0,576460752303423487,0,9223372036854775807,0
%N A266218 Decimal representation of the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
%D A266218 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266218 Robert Price, <a href="/A266218/b266218.txt">Table of n, a(n) for n = 0..499</a>
%H A266218 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266218 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266218 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266218 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,17,0,-16).
%F A266218 From _Colin Barker_, Dec 25 2015 and Apr 13 2019: (Start)
%F A266218 a(n) = 17*a(n-2) - 16*a(n-4) for n>5.
%F A266218 G.f.: (1+6*x-17*x^2+25*x^3+16*x^4-16*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F A266218 (End)
%F A266218 a(n) = (2*4^n - 1)*(n mod 2) + 0^n - 0^abs(n-1). - _Karl V. Keller, Jr._, Aug 17 2021
%t A266218 rule=7; 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 *)
%o A266218 (Python) print([(2*4**n-1)*(n%2) + 0**n - 0**abs(n-1) for n in range(33)]) # _Karl V. Keller, Jr._, Aug 17 2021
%Y A266218 Cf. A266216, A266217.
%K A266218 nonn,easy
%O A266218 0,2
%A A266218 _Robert Price_, Dec 24 2015