A267872 - OEIS

%I #22 Apr 20 2019 05:33:43

%S 1,1,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,

%T 49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,

%U 95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125

%N Number of ON (black) cells in the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell.

%C a(n) = A247328(n+1) for 2 <= n < 472, but a(472) = 945 differs from A247328(473) = 947. Furthermore, a(n) = A163985(n+1) for 2 <= n <= 1000. - _Georg Fischer_, Oct 22 2018

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

%H Robert Price, <a href="/A267872/b267872.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 22 2016 and Apr 20 2019: (Start)

%F a(n) = 2*a(n-1)-a(n-2) for n>3.

%F G.f.: (1-x+4*x^2-2*x^3) / (1-x)^2.

%F (End)

%t rule=237; 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[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)

%Y Cf. A163985, A267870.

%K nonn,easy

%O 0,3

%A _Robert Price_, Jan 21 2016