cp's OEIS Frontend

A266175 Binary representation of the n-th iteration of the "Rule 5" elementary cellular automaton starting with a single ON (black) cell.

%I A266175 #38 Feb 16 2025 08:33:28
%S A266175 1,10,100,1101011,10000,11110101111,1000000,111111010111111,100000000,
%T A266175 1111111101011111111,10000000000,11111111110101111111111,
%U A266175 1000000000000,111111111111010111111111111,100000000000000,1111111111111101011111111111111,10000000000000000
%N A266175 Binary representation of the n-th iteration of the "Rule 5" elementary cellular automaton starting with a single ON (black) cell.
%D A266175 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266175 Robert Price, <a href="/A266175/b266175.txt">Table of n, a(n) for n = 0..999</a>
%H A266175 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266175 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A266175 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266175 <a href="/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266175 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,10101,0,-1010100,0,1000000).
%F A266175 From _Colin Barker_, Dec 23 2015 and Apr 13 2019: (Start)
%F A266175 a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n>5.
%F A266175 G.f.: (1+10*x-10001*x^2+1000001*x^3+10000*x^4-1110000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
%F A266175 (End)
%F A266175 a(n) = floor(10*100^n/9) - 101*10^(n-1) for odd n; a(n) = 10^n = A011557(n) for even n. - _Karl V. Keller, Jr._, Jun 29 2021
%t A266175 rule = 5; 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}]
%o A266175 (Magma) I:=[1,10,100,1101011,10000,11110101111]; [n le 6 select I[n] else 10101*Self(n-2)-1010100*Self(n-4)+1000000*Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Dec 24 2015
%o A266175 (Python) print([10*100**n//9 - 101*10**(n-1) if n%2 else 10**n for n in range(30)]) # _Karl V. Keller, Jr._, Jun 29 2021
%Y A266175 Cf. A266174, A266176.
%Y A266175 Cf. A011557.
%K A266175 nonn,easy
%O A266175 0,2
%A A266175 _Robert Price_, Dec 22 2015