A267940 Binary representation of the n-th iteration of the "Rule 253" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 11111, 1111111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111

Offset

0,2

Comments

With the exception of a(1) the same as A267937, A267889, A267887 and A100706. - R. J. Mathar, Jan 24 2016

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 23 2016 and Apr 16 2019: (Start)

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

G.f.: (1-90*x+10100*x^2-10000*x^3) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=253; 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. A060576.

Sequence in context: A068224 A066945 A267359 * A113615 A034873 A075854

Adjacent sequences: A267937 A267938 A267939 * A267941 A267942 A267943

Keyword

nonn,easy,changed

Author

Robert Price, Jan 22 2016

Status

approved