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%I #21 Sep 14 2021 12:02:52
%S 1,6,7,122,31,2018,95,32738,95,524258,95,8388578,95,134217698,95,
%T 2147483618,95,34359738338,95,549755813858,95,8796093022178,95,
%U 140737488355298,95,2251799813685218,95,36028797018963938,95,576460752303423458,95,9223372036854775778
%N Decimal representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267255/b267255.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>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,17,0,-16).
%F From _Colin Barker_, Jan 13 2016 and Apr 19 2019: (Start)
%F a(n) = 17*a(n-2)-16*a(n-4) for n>8.
%F G.f.: (1+6*x-10*x^2+20*x^3-72*x^4+40*x^5-320*x^6+384*x^7-1024*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%F a(n) = 2*4^n - 30 for odd n>4; a(n) = 95 for even n>4. - _Karl V. Keller, Jr._, Sep 12 2021
%t rule=111; 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 *)
%o (Python) print([1, 6, 7, 122, 31] + [2*4**n - 30 if n%2 else 95 for n in range(5,50)]) # _Karl V. Keller, Jr._, Sep 12 2021
%Y Cf. A267253, A267254.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 12 2016
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