A265380 Binary representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 1110, 11101, 111011, 1110111, 11101110, 111011101, 1110111011, 11101110111, 111011101110, 1110111011101, 11101110111011, 111011101110111, 1110111011101110, 11101110111011101, 111011101110111011, 1110111011101110111, 11101110111011101110

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

Formula

Conjectures from Colin Barker, Dec 14 2015 and Apr 18 2019: (Start)

a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5) for n>4.

G.f.: (1+x+x^2) / ((1-x)*(1+x)*(1-10*x)*(1+x^2)).

(End)

Example

From Michael De Vlieger, Dec 09 2015: (Start)
First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row :
                        (1)                          -> 1
                      1 (1) 1                        -> 11
                    1 1 (1) 0 1                      -> 111
                  1 1 1 (0) 0 1 1                    -> 1110
                1 1 1 0 (1) 1 1 0 1                  -> 11101
              1 1 1 0 0 (1) 1 0 0 1 1                -> 111011
            1 1 1 0 1 1 (1) 0 1 1 1 0 1              -> 1110111
          1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1            -> 11101110
        1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1          -> 111011101
      1 1 1 0 0 1 1 0 0 (1) 1 0 0 1 1 0 0 1 1        -> 1110111011
    1 1 1 0 1 1 1 0 1 1 (1) 0 1 1 1 0 1 1 1 0 1      -> 11101110111
  1 1 1 0 0 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 0 0 1 1    -> 111011101110
1 1 1 0 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 1 1 0 1  -> 1110111011101
(End)

Mathematica

f[n_] := Block[{w = {}}, Do[AppendTo[w, Boole[Mod[k, 4] != 3]], {k, 0, n}]; FromDigits@ w]; Table[f@ n, {n, 0, 19}] (* Michael De Vlieger, Dec 09 2015 *)

Prog

(

Crossrefs

Cf. A071037, A265381.

Sequence in context: A266592 A267209 A110444 * A114397 A336325 A098595

Adjacent sequences: A265377 A265378 A265379 * A265381 A265382 A265383

Keyword

nonn,easy

Author

Robert Price, Dec 07 2015

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed 2 programs based on conjectures. - N. J. A. Sloane, Jun 13 2022

Status

approved