|
%I #43 Jun 13 2022 20:50:26
%S 1,111,11011,1110111,110101011,11101010111,1101010101011,
%T 111010101010111,11010101010101011,1110101010101010111,
%U 110101010101010101011,11101010101010101010111,1101010101010101010101011,111010101010101010101010111,11010101010101010101010101011
%N a(n) = n-th state of cellular automaton generated by "Rule 94" when started with a single ON cell.
%C a(n) has length 2n+1.
%H Robert Price, <a href="/A071033/b071033.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule94.html">Rule 94</a>
%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; Chapter 3.
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to 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 Conjecture: a(n) = floor((1099*100^n + 9090)/990) + 1 for odd n > 1; a(n) = floor((1090*100^n + 10)/990) + 1 for even n > 1. - _Karl V. Keller, Jr._, Oct 25 2021
%t rule=94; 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 *) (* _Robert Price_, Feb 21 2016 *)
%Y This sequence, A118101 and A118102 are equivalent descriptions of the Rule 94 automaton.
%K nonn,easy
%O 0,2
%A _Hans Havermann_, May 26 2002
%E Corrected by _Hans Havermann_, Jan 07 2012
%E Edited by _N. J. A. Sloane_, Oct 20 2015 at the suggestion of _Michael De Vlieger_ and Kevin Ryde
%E More terms from _Robert Price_, Dec 06 2015
| 