A266245 - OEIS

%I #20 Aug 19 2021 09:48:07

%S 1,0,5,96,29,1952,29,32672,29,524192,29,8388512,29,134217632,29,

%T 2147483552,29,34359738272,29,549755813792,29,8796093022112,29,

%U 140737488355232,29,2251799813685152,29,36028797018963872,29,576460752303423392,29,9223372036854775712

%N Decimal representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A266245/b266245.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 14 2019: (Start)

%F a(n) = 17*a(n-2)-16*a(n-4) for n>7.

%F G.f.: (1-12*x^2+96*x^3-40*x^4+320*x^5-384*x^6+1024*x^7) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

%F (End)

%F a(n) = 4^n/2 + 90*floor(4^n/60) - 90 for odd n>3; a(n) = 29 for even n>3. - _Karl V. Keller, Jr._, Aug 17 2021

%t rule=9; 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, 0, 5, 96]+[4**n//2 + 90*(4**n//60) - 90 if n%2 else 29 for n in range(4,50)]) # _Karl V. Keller, Jr._, Aug 17 2021

%Y Cf. A266243, A266244.

%K nonn,easy

%O 0,3

%A _Robert Price_, Dec 25 2015