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%I #29 Apr 15 2019 14:40:08
%S 1,3,0,7,0,11,0,15,0,19,0,23,0,27,0,31,0,35,0,39,0,43,0,47,0,51,0,55,
%T 0,59,0,63,0,67,0,71,0,75,0,79,0,83,0,87,0,91,0,95,0,99,0,103,0,107,0,
%U 111,0,115,0,119,0,123,0,127,0,131,0,135,0,139,0
%N Number of ON (black) cells in the n-th iteration of the "Rule 23" 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="/A266437/b266437.txt">Table of n, a(n) for n = 0..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</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 Empirical g.f.: (1 + 3*x - 2*x^2 + x^3 + x^4)/(-1 + x^2)^2. - _Michael De Vlieger_, Dec 29 2015
%F Conjectures from _Colin Barker_, Dec 30 2015 and Apr 15 2019: (Start)
%F a(n) = (1-(-1)^n)*(2*n+1)/2 for n>0.
%F a(n) = 2*a(n-2)-a(n-4) for n>4.
%F (End)
%F a(n) = A266220(n), n>1. - _R. J. Mathar_, Jan 10 2016
%t 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 *) Table[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)
%Y Cf. A266434.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015
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