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%I #27 Jul 31 2021 16:38:43
%S 1,7,0,127,0,2047,0,32767,0,524287,0,8388607,0,134217727,0,2147483647,
%T 0,34359738367,0,549755813887,0,8796093022207,0,140737488355327,0,
%U 2251799813685247,0,36028797018963967,0,576460752303423487,0,9223372036854775807,0
%N Decimal representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
%C With the exception of a(1) the same as A266380, A266324 and A266218. - _R. J. Mathar_, Jan 10 2016
%H Robert Price, <a href="/A266436/b266436.txt">Table of n, a(n) for n = 0..500</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_, Dec 30 2015 and Apr 15 2019: (Start)
%F a(n) = ((-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.
%F a(n) = 17*a(n-2)-16*a(n-4) for n>4.
%F G.f.: (1+7*x-17*x^2+8*x^3+16*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%F a(n) = (2*4^n-1)*(n mod 2) + 0^n. - _Karl V. Keller, Jr._, Jul 06 2021
%t rule=23; 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([(2*4**n-1)*(n%2) + 0**n for n in range(33)]) # _Karl V. Keller, Jr._, Jul 06 2021
%Y Cf. A241955, A266434, A266435 (binary).
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015