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%I #13 Apr 19 2019 14:48:30
%S 0,2,5,10,15,23,30,40,51,63,75,91,106,123,141,161,181,204,226,251,277,
%T 304,331,362,392,424,457,492,527,565,602,642,683,725,767,813,858,905,
%U 953,1003,1053,1106,1158,1213,1269,1326,1383,1444,1504,1566,1629,1694
%N Total number of OFF (white) cells after n iterations of the "Rule 131" 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="/A267454/b267454.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 15 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.: x*(2+3*x+5*x^2+3*x^3+3*x^4-x^5) / ((1-x)^3*(1+x)*(1+x^2)*(1+x+x^2)).
%F (End)
%t rule=131; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)
%Y Cf. A267418.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 15 2016
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