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Number of ON (black) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
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%I #19 Apr 18 2019 16:52:59

%S 1,2,2,5,4,7,5,11,5,15,5,19,5,23,5,27,5,31,5,35,5,39,5,43,5,47,5,51,5,

%T 55,5,59,5,63,5,67,5,71,5,75,5,79,5,83,5,87,5,91,5,95,5,99,5,103,5,

%U 107,5,111,5,115,5,119,5,123,5,127,5,131,5,135,5,139

%N Number of ON (black) cells in the n-th iteration of the "Rule 61" 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="/A266792/b266792.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 04 2016 and Apr 18 2019: (Start)

%F a(n) = n+1-(-1)^n*(n-4) for n>4.

%F a(n) = 2*a(n-2)-a(n-4) for n>8.

%F G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^2*(1+x)^2).

%F (End)

%t rule=61; 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. A266786.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 03 2016