A267526 - OEIS

%I #43 Jun 14 2022 08:18:13

%S 1,10,101,1011,1010111,10101111,10101011111,101010111111,

%T 101010101111111,1010101011111111,1010101010111111111,

%U 10101010101111111111,10101010101011111111111,101010101010111111111111,101010101010101111111111111,1010101010101011111111111111

%N Binary representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267526/b267526.txt">Table of n, a(n) for n = 0..1000</a>

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

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%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>

%F Conjectures from _Colin Barker_, Jan 16 2016: (Start)

%F a(n) = 11*a(n-1) + 9990*a(n-2) - 110000*a(n-3) + 100000*a(n-4) for n > 5.

%F G.f.: (1 - x - 9999*x^2 + 10000*x^3 + 990000*x^4 - 1000000*x^5) / ((1-x)*(1-10*x)*(1-100*x)*(1+100*x)). - [corrected by _Karl V. Keller, Jr._, Sep 18 2021]

%F (End)

%F Conjecture: a(n) = 10^n*(100^floor(n/2) - 1)/99 + (10^(n-1) - 1)/9 for n > 1. - _Karl V. Keller, Jr._, Sep 22 2021

%t rule=141; 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 *)

%Y Cf. A267525, A267527.

%K nonn

%O 0,2

%A _Robert Price_, Jan 16 2016