A267876 Binary representation of the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 10101, 1110111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111

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 22 2016 and Apr 20 2019: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>3.

G.f.: (1-101*x+10201*x^2+89910*x^3-100000*x^5) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=233; 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. A267868.

Sequence in context: A258189 A114385 A267680 * A353110 A144863 A300558

Adjacent sequences: A267873 A267874 A267875 * A267877 A267878 A267879

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved