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

1, 10, 100, 1001, 10010, 100101, 1001010, 10010101, 100101010, 1001010101, 10010101010, 100101010101, 1001010101010, 10010101010101, 100101010101010, 1001010101010101, 10010101010101010, 100101010101010101, 1001010101010101010, 10010101010101010101

Offset

0,2

References

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

Links

Robert Price, Table of n, a(n) for n = 0..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

Formula

G.f.: (1 - x^2 + x^3)/(1 - 10*x - x^2 + 10*x^3). - Michael De Vlieger, Dec 21 2015

a(n) = floor(991*10^n/990). - Karl V. Keller, Jr., Oct 09 2021

Example

From Michael De Vlieger, Dec 21 2015: (Start)
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:
              (1)               ->         1
            1 (0) 0             ->        10
          0 0 (0) 1 0           ->       100
        1 1 1 (1) 0 0 1         ->      1001
      0 0 0 0 (0) 0 1 0 0       ->     10010
    1 1 1 1 1 (1) 1 0 0 1 1     ->    100101
  0 0 0 0 0 0 (0) 0 0 1 0 0 0   ->   1001010
1 1 1 1 1 1 1 (1) 1 1 0 0 1 1 1 ->  10010101
(End)

Mathematica

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 *)

Prog

(Python) print([991*10**n//990 for n in range(50)]) # Karl V. Keller, Jr., Oct 09 2021

Crossrefs

Cf. A266070, A081253 (decimal).

Sequence in context: A281730 A282954 A282984 * A118256 A351386 A102397

Adjacent sequences: A266068 A266069 A266070 * A266072 A266073 A266074

Keyword

nonn,easy

Author

Robert Price, Dec 20 2015

Status

approved