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%I #15 Apr 18 2019 16:53:05
%S 1,3,5,10,14,21,26,37,42,57,62,81,86,109,114,141,146,177,182,217,222,
%T 261,266,309,314,361,366,417,422,477,482,541,546,609,614,681,686,757,
%U 762,837,842,921,926,1009,1014,1101,1106,1197,1202,1297,1302,1401,1406
%N Total number of ON (black) cells after n iterations 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="/A266793/b266793.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) = (1+7*(-1)^n-2*(-3+(-1)^n)*n+2*n^2)/4 for n>3.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>8.
%F G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(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 *) 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. A266786.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 03 2016
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