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%I #33 Jul 06 2023 12:32:59
%S 1,10,100,1000,10001,100010,1000101,10001010,100010101,1000101011,
%T 10001010110,100010101100,1000101011000,10001010110001,
%U 100010101100010,1000101011000101,10001010110001010,100010101100010101,1000101011000101010,10001010110001010101
%N Binary representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
%D Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A266445/b266445.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 <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_, Dec 31 2015 and Apr 16 2019: (Start)
%F a(n) = (-9*(-1)^n+9901000008901*2^(n-10)*5^(n-11)-11)/198 for n>10.
%F G.f.: (1-x^2+x^4+x^9-x^10-x^11+x^13) / ((1-x)*(1+x)*(1-10*x)).
%F (End)
%F Conjecture: a(n) = floor(9901000008901*10^n/9900000000000). - _Karl V. Keller, Jr._, Jan 30 2022
%t rule=25; 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]],{k,1,rows}] (* Binary Representation of Middle Column *)
%Y Cf. A266441, A266444, A266446.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015
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