cp's OEIS Frontend

A266071 Binary representation of the middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

%I A266071 #22 Feb 16 2025 08:33:28
%S A266071 1,10,100,1001,10010,100101,1001010,10010101,100101010,1001010101,
%T A266071 10010101010,100101010101,1001010101010,10010101010101,
%U A266071 100101010101010,1001010101010101,10010101010101010,100101010101010101,1001010101010101010,10010101010101010101
%N A266071 Binary representation of the middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
%D A266071 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266071 Robert Price, <a href="/A266071/b266071.txt">Table of n, a(n) for n = 0..999</a>
%H A266071 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266071 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266071 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266071 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-10).
%F A266071 G.f.: (1 - x^2 + x^3)/(1 - 10*x - x^2 + 10*x^3). - _Michael De Vlieger_, Dec 21 2015
%F A266071 a(n) = floor(991*10^n/990). - _Karl V. Keller, Jr._, Oct 09 2021
%e A266071 From _Michael De Vlieger_, Dec 21 2015: (Start)
%e A266071 First 8 rows at left with the center column values in parentheses, and at right the binary value of center column cells up to that row:
%e A266071               (1)               ->         1
%e A266071             1 (0) 0             ->        10
%e A266071           0 0 (0) 1 0           ->       100
%e A266071         1 1 1 (1) 0 0 1         ->      1001
%e A266071       0 0 0 0 (0) 0 1 0 0       ->     10010
%e A266071     1 1 1 1 1 (1) 1 0 0 1 1     ->    100101
%e A266071   0 0 0 0 0 0 (0) 0 0 1 0 0 0   ->   1001010
%e A266071 1 1 1 1 1 1 1 (1) 1 1 0 0 1 1 1 ->  10010101
%e A266071 (End)
%t A266071 Table[SeriesCoefficient[(1 - x^2 + x^3)/(1 - 10 x - x^2 + 10 x^3), {x, 0, n}], {n, 0, 19}] (* _Michael De Vlieger_, Dec 21 2015 *)
%o A266071 (Python) print([991*10**n//990 for n in range(50)]) # _Karl V. Keller, Jr._, Oct 09 2021
%Y A266071 Cf. A266070, A081253 (decimal).
%K A266071 nonn,easy
%O A266071 0,2
%A A266071 _Robert Price_, Dec 20 2015