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%I #26 Sep 02 2021 19:17:32
%S 1,6,1,126,1,2046,1,32766,1,524286,1,8388606,1,134217726,1,2147483646,
%T 1,34359738366,1,549755813886,1,8796093022206,1,140737488355326,1,
%U 2251799813685246,1,36028797018963966,1,576460752303423486,1,9223372036854775806,1
%N Decimal representation of the n-th iteration of the "Rule 15" 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="/A266302/b266302.txt">Table of n, a(n) for n = 0..999</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>
%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 28 2015 and Apr 15 2019: (Start)
%F a(n) = (3*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2.
%F a(n) = 17*a(n-2)-16*a(n-4) for n>3.
%F G.f.: (1+6*x-16*x^2+24*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%F a(n) = 2*4^n - 2 for odd n; a(n) = 1 for even n. - _Karl V. Keller, Jr._, Aug 31 2021
%F E.g.f.: cosh(x) - 2*sinh(x) + 2*sinh(4*x). - _Stefano Spezia_, Sep 01 2021
%t rule=15; 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 - 2 if n%2 else 1 for n in range(50)]) # _Karl V. Keller, Jr._, Aug 31 2021
%Y Cf. A266300, A266301.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 26 2015
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