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%I #16 Apr 16 2019 06:27:06
%S 0,2,3,4,5,5,9,5,13,5,17,5,21,5,25,5,29,5,33,5,37,5,41,5,45,5,49,5,53,
%T 5,57,5,61,5,65,5,69,5,73,5,77,5,81,5,85,5,89,5,93,5,97,5,101,5,105,5,
%U 109,5,113,5,117,5,121,5,125,5,129,5,133,5,137,5
%N Number of OFF (white) cells in the n-th iteration of the "Rule 25" 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="/A266449/b266449.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_, Dec 30 2015 and Apr 16 2019: (Start)
%F a(n) = (-1)^n*(n-4)+n+1 for n>3.
%F a(n) = 2*a(n-2)-a(n-4) for n>7.
%F G.f.: x*(1+x-x^2)*(2+x+x^2-x^3+x^4) / ((1-x)^2*(1+x)^2).
%F (End)
%t rule=25; 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[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y Cf. A266441.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015
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