A267211 - OEIS

%I #15 Apr 19 2019 09:52:28

%S 1,1,5,2,7,7,10,5,13,12,13,11,18,15,19,16,21,21,24,19,27,26,27,25,32,

%T 29,33,30,35,35,38,33,41,40,41,39,46,43,47,44,49,49,52,47,55,54,55,53,

%U 60,57,61,58,63,63,66,61,69,68,69,67,74,71,75,72,77,77

%N Number of ON (black) cells in the n-th iteration of the "Rule 109" 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="/A267211/b267211.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 13 2016: (Start)

%F a(n) = a(n-3)+a(n-4)-a(n-7) for n>7.

%F G.f.: (1+x+5*x^2+x^3+5*x^4+x^5+3*x^6-3*x^7) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).

%F (End)

%t rule=109; 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. A243566.

%K nonn,easy

%O 0,3

%A _Robert Price_, Jan 11 2016