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A267212 Total number of ON (black) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell. 1

%I #15 Apr 19 2019 09:52:25

%S 1,2,7,9,16,23,33,38,51,63,76,87,105,120,139,155,176,197,221,240,267,

%T 293,320,345,377,406,439,469,504,539,577,610,651,691,732,771,817,860,

%U 907,951,1000,1049,1101,1148,1203,1257,1312,1365,1425,1482,1543,1601

%N Total number of ON (black) cells after n iterations 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="/A267212/b267212.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 and Apr 19 2019: (Start)

%F a(n) = a(n-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) 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)^3*(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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc,k]],{k,1,rows}] (* Number of Black cells through stage n *)

%Y Cf. A243566.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 11 2016

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)