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%I #15 Feb 26 2023 19:35:33
%S 1,1,2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,35,
%T 36,38,39,41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,63,65,66,68,69,
%U 71,72,74,75,77,78,80,81,83,84,86,87,89,90,92,93,95,96,98
%N Number of ON (black) cells in the n-th iteration of the "Rule 141" 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="/A267528/b267528.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 16 2016 and Apr 17 2019: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.
%F G.f.: (1 + x^3 + x^4)/((1 - x)^2*(1 + x)). (End)
%F Conjectured e.g.f.: 2 + x + (3*x/2 - 1)*cosh(x) + 3*(x - 1)*sinh(x)/2. - _Stefano Spezia_, Feb 20 2023
%t rule=141; 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. A267525.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 16 2016
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