A265379 - OEIS

%I #32 Sep 21 2021 06:34:42

%S 1,111,11101,1110011,111011101,11100110011,1110111011101,

%T 111001100110011,11101110111011101,1110011001100110011,

%U 111011101110111011101,11100110011001100110011,1110111011101110111011101,111001100110011001100110011,11101110111011101110111011101

%N Binary representation of the n-th iteration of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A265379/b265379.txt">Table of n, a(n) for n = 0..499</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule158.html">Rule 158</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10001,0,-10000).

%F From _Colin Barker_, Dec 14 2015 and Apr 18 2019: (Start)

%F a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

%F G.f.: (1+111*x+1100*x^2-100*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

%F (End)

%F a(n) = floor((11100 - (n mod 2))*100^n/9999). - _Karl V. Keller, Jr._, Sep 20 2021

%e From _Michael De Vlieger_, Dec 09 2015: (Start)

%e First 12 rows:

%e                         1

%e                       1 1 1

%e                     1 1 1 0 1

%e                   1 1 1 0 0 1 1

%e                 1 1 1 0 1 1 1 0 1

%e               1 1 1 0 0 1 1 0 0 1 1

%e             1 1 1 0 1 1 1 0 1 1 1 0 1

%e           1 1 1 0 0 1 1 0 0 1 1 0 0 1 1

%e         1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1

%e       1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

%e     1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1

%e   1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

%e 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1

%e (End)

%t rule = 158; 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 (Python) print([(11100 - (n%2))*100**n//9999 for n in range(30)]) # _Karl V. Keller, Jr._, Sep 20 2021

%Y Cf. A071037 (cells), A118171 (decimal).

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 07 2015