A267775 Binary representation of the n-th iteration of the "Rule 207" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 11101, 1111011, 111110111, 11111101111, 1111111011111, 111111110111111, 11111111101111111, 1111111111011111111, 111111111110111111111, 11111111111101111111111, 1111111111111011111111111, 111111111111110111111111111, 11111111111111101111111111111

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

Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start)

a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3.

G.f.: (1-x+x^2-100*x^3) / ((1-x)*(1-10*x)*(1-100*x)).

(End)

Mathematica

rule=207; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}]   (* Binary Representation of Rows *)

Crossrefs

Cf. A267773, A267774.

Sequence in context: A211979 A135650 A193240 * A267867 A267889 A285696

Adjacent sequences: A267772 A267773 A267774 * A267776 A267777 A267778

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved