|
%I #22 Aug 21 2021 16:06:31
%S 1,10,100,1001,10011,100110,1001100,10011001,100110011,1001100110,
%T 10011001100,100110011001,1001100110011,10011001100110,
%U 100110011001100,1001100110011001,10011001100110011,100110011001100110,1001100110011001100,10011001100110011001
%N Binary representation of the middle column of the "Rule 147" 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="/A262863/b262863.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 From _Colin Barker_, Jan 17 2016 and Apr 17 2019: (Start)
%F a(n) = 11*a(n-1)-11*a(n-2)+11*a(n-3)-10*a(n-4) for n>3.
%F G.f.: (1-x+x^2) / ((1-x)*(1-10*x)*(1+x^2)).
%F (End)
%F a(n) = floor(100100*10^n/99990). - _Karl V. Keller, Jr._, Aug 21 2021
%t rule=147; 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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}] (* Binary Representation of Middle Column *)
%o (Python) print([100100*10**n//99990 for n in range(50)]) # _Karl V. Keller, Jr._, Aug 21 2021
%Y Cf. A262808, A262864.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 17 2016
|
