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%I #26 Jul 06 2023 12:35:29
%S 1,10,1110,1000001,111000,11100000111,11100000,111110000011111,
%T 1110000000,1111111000001111111,111000000000,11111111100000111111111,
%U 11100000000000,111111111110000011111111111,1110000000000000,1111111111111000001111111111111,111000000000000000
%N Binary representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A266589/b266589.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 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%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 01 2016 and Apr 18 2019: (Start)
%F a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>7.
%F G.f.: (1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).
%F (End)
%F Conjecture: a(n) = (10*100^n - 99999*10^(n-2) - 1)/9 for odd n > 1; a(n) = 111*10^(n-1) for even n > 1. - _Karl V. Keller, Jr._, Oct 06 2021
%t rule=37; 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[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)
%Y Cf. A266588, A266590.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 01 2016
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