%I #21 Feb 16 2025 08:33:28
%S 0,1,3,2,5,4,8,4,12,4,16,4,20,4,24,4,28,4,32,4,36,4,40,4,44,4,48,4,52,
%T 4,56,4,60,4,64,4,68,4,72,4,76,4,80,4,84,4,88,4,92,4,96,4,100,4,104,4,
%U 108,4,112,4,116,4,120,4,124,4,128,4,132,4,136,4
%N Number of OFF (white) 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="/A266794/b266794.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://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 17 2019: (Start)
%F a(n) = n+(-1)^n*(n-4) for n>4.
%F a(n) = 2*a(n-2)-a(n-4) for n>7.
%F G.f.: x*(1+3*x-x^3+x^4+x^5-2*x^6+x^7) / ((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 *) 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. A266786.
%Y Cf. A266795 (partial sums).
%K nonn,easy,changed
%O 0,3
%A _Robert Price_, Jan 03 2016