A266219 Binary representation of the middle column of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 110, 1101, 11010, 110101, 1101010, 11010101, 110101010, 1101010101, 11010101010, 110101010101, 1101010101010, 11010101010101, 110101010101010, 1101010101010101, 11010101010101010, 110101010101010101, 1101010101010101010, 11010101010101010101

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..499

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 25 2015 and Apr 13 2019: (Start)

a(n) = 1/198*(-9*(-1)^n+109*2^(n+1)*5^n-11).

a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.

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

(End)

Conjecture: a(n) = floor(109*10^n/99). - Karl V. Keller, Jr., Mar 16 2022

Mathematica

rule=7; 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. A266216, A081254.

Sequence in context: A272609 A267366 A101556 * A267580 A280561 A281281

Adjacent sequences: A266216 A266217 A266218 * A266220 A266221 A266222

Keyword

nonn,easy,changed

Author

Robert Price, Dec 24 2015

Status

approved