A267680 Binary representation of the n-th iteration of the "Rule 201" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 10101, 1100011, 111010111, 11110001111, 1111101011111, 111111000111111, 11111110101111111, 1111111100011111111, 111111111010111111111, 11111111110001111111111, 1111111111101011111111111, 111111111111000111111111111, 11111111111110101111111111111

Offset

0,3

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 19 2016 and Apr 20 2019: (Start)

a(n) = 101*a(n-1)-10100*a(n-3)+10000*a(n-4) for n>4.

G.f.: (1-101*x+10101*x^2+89910*x^3-101000*x^4) / ((1-x)*(1-10*x)*(1+10*x)*(1-100*x)).

(End)

Mathematica

rule=201; 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. A267679, A267681.

Sequence in context: A210892 A258189 A114385 * A267876 A353110 A144863

Adjacent sequences: A267677 A267678 A267679 * A267681 A267682 A267683

Keyword

nonn,easy

Author

Robert Price, Jan 19 2016

Status

approved