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%I #30 Jul 06 2023 13:16:54
%S 1,3,28,47,496,575,8000,9215,128000,147455,2048000,2359295,32768000,
%T 37748735,524288000,603979775,8388608000,9663676415,134217728000,
%U 154618822655,2147483648000,2473901162495,34359738368000,39582418599935,549755813888000,633318697598975
%N Decimal representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267360/b267360.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 14 2016 and Apr 19 2019: (Start)
%F a(n) = 17*a(n-2)-16*a(n-4) for n>8.
%F G.f.: (1+3*x+11*x^2-4*x^3+36*x^4-176*x^5+16*x^6+192*x^7-64*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=125; 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]],2],{k,1,rows}] (* decimal representation of rows *)
%Y Cf. A267358, A267359.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 13 2016
%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022
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