A266787 - OEIS

%I #34 Feb 16 2025 08:33:28

%S 1,11,1100,1010111,1111000,11010001111,1111010000,111010001111111,

%T 1111010000000,1111010001111111111,1111010000000000,

%U 11111010001111111111111,1111010000000000000,111111010001111111111111111,1111010000000000000000,1111111010001111111111111111111

%N Binary representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266787/b266787.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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>

%F Conjectures from _Colin Barker_, Jan 03 2016 and Apr 18 2019: (Start)

%F a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>10.

%F G.f.: (1 +11*x -9901*x^2 +889100*x^3 -979100*x^4 +7891000*x^5 -109001000*x^6 +1090110000*x^7 +9990000*x^8 -1100000000*x^9 +100000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -1000*x^2)).

%F (End)

%t rule=61; 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. A266786, A266788.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 03 2016