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 A266324 #31 Aug 08 2025 12:09:38
%S A266324 1,5,0,127,0,2047,0,32767,0,524287,0,8388607,0,134217727,0,2147483647,
%T A266324 0,34359738367,0,549755813887,0,8796093022207,0,140737488355327,0,
%U A266324 2251799813685247,0,36028797018963967,0,576460752303423487,0,9223372036854775807,0
%N A266324 Decimal representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell.
%D A266324 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266324 Robert Price, <a href="/A266324/b266324.txt">Table of n, a(n) for n = 0..500</a>
%H A266324 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266324 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266324 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266324 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,17,0,-16).
%F A266324 From _Colin Barker_, Dec 28 2015 and Apr 15 2019: (Start)
%F A266324 a(n) = 17*a(n-2) - 16*a(n-4) for n>5.
%F A266324 G.f.: (1+5*x-17*x^2+42*x^3+16*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)). (End)
%F A266324 a(n) = (1-(-1)^n)*(4*16^floor(n/2)-1/2) for n>1. - _Bruno Berselli_, Dec 29 2015
%F A266324 a(n) = (2*4^n - 1)*(n mod 2) + 0^n - 2*0^abs(n-1). - _Karl V. Keller, Jr._, Sep 02 2021
%F A266324 E.g.f.: 1 - 2*x - sinh(x) + 2*sinh(4*x). - _Stefano Spezia_, Sep 03 2021
%t A266324 rule=19; 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 A266324 (Magma) [n le 1 select 5^n else (1-(-1)^n)*(4*16^Floor(n/2)-1/2): n in [0..40]]; // _Bruno Berselli_, Dec 29 2015
%o A266324 (Python) print([(2*4**n - 1)*(n%2) + 0**n - 2*0**abs(n-1) for n in range(50)]) # _Karl V. Keller, Jr._, Sep 02 2021
%Y A266324 Cf. A266155, A266323. Essentially the same as A266218.
%K A266324 nonn,easy
%O A266324 0,2
%A A266324 _Robert Price_, Dec 27 2015