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

Author

Robert Price, Dec 20 2015

Keywords

• nonn
• easy

Examples

			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)
		

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).

Crossrefs

Cf. A266070, A081253 (decimal).

Programs

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 *)

Python

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

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