A267801 Binary representation of the n-th iteration of the "Rule 213" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 10011, 1110011, 111110011, 11111110011, 1111111110011, 111111111110011, 11111111111110011, 1111111111111110011, 111111111111111110011, 11111111111111111110011, 1111111111111111111110011, 111111111111111111111110011, 11111111111111111111111110011

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 21 2016 and Apr 20 2019: (Start)

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

G.f.: (1+10*x)*(1-100*x+10000*x^2) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=213; 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. A267800.

Sequence in context: A286647 A267035 A204574 * A050647 A267054 A082265

Adjacent sequences: A267798 A267799 A267800 * A267802 A267803 A267804

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Status

approved