cp's OEIS Frontend

A266379 Binary representation of the n-th iteration of the "Rule 21" elementary cellular automaton starting with a single ON (black) cell.

%I A266379 #35 Aug 08 2025 12:12:56
%S A266379 1,11,0,1111111,0,11111111111,0,111111111111111,0,1111111111111111111,
%T A266379 0,11111111111111111111111,0,111111111111111111111111111,0,
%U A266379 1111111111111111111111111111111,0,11111111111111111111111111111111111,0,111111111111111111111111111111111111111
%N A266379 Binary representation of the n-th iteration of the "Rule 21" elementary cellular automaton starting with a single ON (black) cell.
%H A266379 Robert Price, <a href="/A266379/b266379.txt">Table of n, a(n) for n = 0..500</a>
%H A266379 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266379 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266379 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266379 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266379 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10001,0,-10000).
%F A266379 From _Colin Barker_, Dec 29 2015: (Start)
%F A266379 a(n) = 10001*a(n-2) - 10000*a(n-4) for n>5.
%F A266379 G.f.: (1 + 11*x - 10001*x^2 + 1001100*x^3 + 10000*x^4 - 1000000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)). (End)
%F A266379 a(n) = (1-(-1)^n)*(1000*10000^floor(n/2)-1)/18 for n>1. - _Bruno Berselli_, Dec 29 2015
%F A266379 a(n) = (10*100^n - 1)/9*(n mod 2) + 0^n - 100*0^abs(n-1). - _Karl V. Keller, Jr._, Sep 03 2021
%t A266379 rule=21; 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 *)
%o A266379 (Magma) [n le 1 select 11^n else (1-(-1)^n)*(1000*10000^Floor(n/2)-1)/18: n in [0..40]]; // _Bruno Berselli_, Dec 29 2015
%o A266379 (Python) print([(10*100**n - 1)//9*(n%2) + 0**n - 100*0**abs(n-1) for n in range(50)]) # _Karl V. Keller, Jr._, Sep 03 2021
%Y A266379 Cf. A266377, A266380.
%Y A266379 Essentially the same as A266217 and A266323.
%K A266379 nonn,easy
%O A266379 0,2
%A A266379 _Robert Price_, Dec 28 2015