A267846 Binary representation of the n-th iteration of the "Rule 227" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 11010, 1111010, 111111010, 11111111010, 1111111111010, 111111111111010, 11111111111111010, 1111111111111111010, 111111111111111111010, 11111111111111111111010, 1111111111111111111111010, 111111111111111111111111010, 11111111111111111111111111010

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: (Start)

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

G.f.: (1-x+1010*x^2+9000*x^3) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=227; 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. A267845.

Sequence in context: A163663 A272681 A267674 * A267684 A267885 A307810

Adjacent sequences: A267843 A267844 A267845 * A267847 A267848 A267849

Keyword

nonn

Author

Robert Price, Jan 21 2016

Status

approved