A267153 - OEIS

%I #21 Jun 13 2022 16:45:35

%S 1,100,1011,1101110,1110111,11110111010,111011011,111111011111110,

%T 11100000111,1111111101011111010,1101100011011,

%U 11111111111111011111110,11100000111,111111111111111101011111010,1101100011011,1111111111111111111111011111110,11100000111

%N Binary representation of the n-th iteration of the "Rule 107" 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="/A267153/b267153.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 11 2016 and Apr 19 2019: (Start)

%F a(n) = 10000*a(n-2)+a(n-4)-10000*a(n-6) for n>12.

%F G.f.: (1 +100*x -8989*x^2 +101110*x^3 -8999890*x^4 +99010910*x^5 -10990090000*x^6 +9900910000*x^7 -1099001110000*x^8 +989801000000*x^9 -109887911000000*x^10 +100990000000000*x^11 -11009890000000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +x^2)).

%F (End)

%t rule=107; 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. A267152, A267154.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 11 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022