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A267045 Decimal representation of the middle column of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

%I A267045 #24 Feb 16 2025 08:33:29
%S A267045 1,2,4,8,17,34,69,138,277,554,1109,2218,4437,8874,17749,35498,70997,
%T A267045 141994,283989,567978,1135957,2271914,4543829,9087658,18175317,
%U A267045 36350634,72701269,145402538,290805077,581610154,1163220309,2326440618,4652881237,9305762474
%N A267045 Decimal representation of the middle column of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
%D A267045 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267045 Robert Price, <a href="/A267045/b267045.txt">Table of n, a(n) for n = 0..1000</a>
%H A267045 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267045 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267045 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267045 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267045 Conjectures from _Colin Barker_, Jan 10 2016 and Apr 17 2019: (Start)
%F A267045 a(n) = (2*(-1)^n+13*2^n-6)/12 for n>1.
%F A267045 a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4. [Typo corrected by _Karl V. Keller, Jr._, Mar 16 2022]
%F A267045 G.f.: (1-x^2+x^4) / ((1-x)*(1+x)*(1-2*x)).
%F A267045 (End)
%t A267045 rule=91; 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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k],2],{k,1,rows}]  (* Binary Representation of Middle Column *)
%Y A267045 Cf. A267015, A267044.
%K A267045 nonn,easy
%O A267045 0,2
%A A267045 _Robert Price_, Jan 09 2016