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A266259 Total number of OFF (white) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

%I A266259 #14 Feb 16 2025 08:33:28
%S A266259 0,2,5,7,14,16,27,29,44,46,65,67,90,92,119,121,152,154,189,191,230,
%T A266259 232,275,277,324,326,377,379,434,436,495,497,560,562,629,631,702,704,
%U A266259 779,781,860,862,945,947,1034,1036,1127,1129,1224,1226,1325,1327,1430
%N A266259 Total number of OFF (white) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
%D A266259 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266259 Robert Price, <a href="/A266259/b266259.txt">Table of n, a(n) for n = 0..999</a>
%H A266259 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266259 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266259 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266259 Conjectures from _Colin Barker_, Dec 27 2015 and Apr 14 2019: (Start)
%F A266259 a(n) = ((n+1)^2+(-1)^n*(n-1))/2.
%F A266259 a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.
%F A266259 G.f.: x*(2+3*x-2*x^2+x^3) / ((1-x)^3*(1+x)^2).
%F A266259 (End)
%t A266259 rule=11; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)
%Y A266259 Cf. A266253.
%K A266259 nonn,easy
%O A266259 0,2
%A A266259 _Robert Price_, Dec 25 2015
%E A266259 Conjectures from _Colin Barker_, Apr 14 2019