A267688 Binary representation of the n-th iteration of the "Rule 199" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 11100, 1111010, 111110100, 11111101010, 1111111010100, 111111110101010, 11111111101010100, 1111111111010101010, 111111111110101010100, 11111111111101010101010, 1111111111111010101010100, 111111111111110101010101010, 11111111111111101010101010100

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 19 2016: (Start)

a(n) = 110*a(n-1) - 999*a(n-2) - 110*a(n-3) + 1000*a(n-4) for n > 4.

G.f.: (1 - x^2 + 10*x^3 - 1000*x^4) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).

(End)

Mathematica

rule=199; 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. A267687, A267689.

Sequence in context: A265320 A109241 A090490 * A211979 A135650 A193240

Adjacent sequences: A267685 A267686 A267687 * A267689 A267690 A267691

Keyword

nonn

Author

Robert Price, Jan 19 2016

Status

approved