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A266439 Number of OFF (white) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.

%I A266439 #24 Feb 16 2025 08:33:28
%S A266439 0,0,5,0,9,0,13,0,17,0,21,0,25,0,29,0,33,0,37,0,41,0,45,0,49,0,53,0,
%T A266439 57,0,61,0,65,0,69,0,73,0,77,0,81,0,85,0,89,0,93,0,97,0,101,0,105,0,
%U A266439 109,0,113,0,117,0,121,0,125,0,129,0,133,0,137,0,141,0
%N A266439 Number of OFF (white) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
%D A266439 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266439 Robert Price, <a href="/A266439/b266439.txt">Table of n, a(n) for n = 0..500</a>
%H A266439 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266439 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A266439 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266439 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266439 Conjectures from _Colin Barker_, Dec 30 2015 and Apr 15 2019: (Start)
%F A266439 a(n) = ((-1)^n+1)*(2*n+1)/2 for n>0.
%F A266439 a(n) = 2*a(n-2)-a(n-4) for n>4.
%F A266439 G.f.: x^2*(5-x^2) / ((1-x)^2*(1+x)^2).
%F A266439 (End)
%F A266439 a(n) = A266222(n), n>1. - _R. J. Mathar_, Jan 10 2016
%t A266439 rule=23; 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 A266439 Cf. A266434.
%K A266439 nonn,easy
%O A266439 0,3
%A A266439 _Robert Price_, Dec 29 2015