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%I #15 Apr 14 2019 11:52:56
%S 1,0,2,2,4,5,4,9,4,13,4,17,4,21,4,25,4,29,4,33,4,37,4,41,4,45,4,49,4,
%T 53,4,57,4,61,4,65,4,69,4,73,4,77,4,81,4,85,4,89,4,93,4,97,4,101,4,
%U 105,4,109,4,113,4,117,4,121,4,125,4,129,4,133,4,137
%N Number of ON (black) cells in the n-th iteration of the "Rule 9" 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="/A266249/b266249.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</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_, Dec 28 2015 and Apr 14 2019: (Start)
%F a(n) = (-2*(-1)^n*n+2*n+9*(-1)^n-1)/2 for n>3.
%F a(n) = 2*a(n-2)-a(n-4) for n>7.
%F G.f.: (1+2*x^3+x^4+x^5-2*x^6+x^7) / ((1-x)^2*(1+x)^2).
%F (End)
%t rule=9; 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. A266243.
%K nonn,easy
%O 0,3
%A _Robert Price_, Dec 25 2015
%E Conjectures from _Colin Barker_, Apr 14 2019
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