A267257 Binary representation of the middle column of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111110, 1111111101, 11111111010, 111111110101, 1111111101010, 11111111010101, 111111110101010, 1111111101010101, 11111111010101010, 111111110101010101, 1111111101010101010, 11111111010101010101

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..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(n) = A007088(A267258(n)). - R. J. Mathar, Apr 12 2019

Conjectures from Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)

a(n) = (-9*(-1)^n+109999999*2^(n-5)*5^(n-6)-11)/198 for n>5.

G.f.: (1+x-x^8) / ((1-x)*(1+x)*(1-10*x)).

(End)

Mathematica

rule=111; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Crossrefs

Cf. A267253.

Sequence in context: A138145 A165370 A134962 * A113589 A366394 A135463

Adjacent sequences: A267254 A267255 A267256 * A267258 A267259 A267260

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved