A265427 Binary representation of the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 101, 1111, 11101, 110111, 1011101, 11110111, 111011101, 1101110111, 10111011101, 111101110111, 1110111011101, 11011101110111, 101110111011101, 1111011101110111, 11101110111011101, 110111011101110111, 1011101110111011101, 11110111011101110111

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..999

Eric Weisstein's World of Mathematics, Rule 188

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 09 2015 and Apr 18 2019: (Start)

a(n) = a(n-2) + 10000*a(n-4) - 10000*a(n-6) for n>5.

G.f.: (1+11*x+100*x^2+1100*x^3+1000*x^4-1000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1+100*x^2)).

(End)

Conjecture: a(n) = floor(11100*100^n/9999) + 10^n - floor(11100*10^n/9999)*10^n. - Karl V. Keller, Jr., Dec 15 2021

Example

From Michael De Vlieger, Dec 09 2015: (Start)
First 12 rows:
1
1 1
1 0 1
1 1 1 1
1 1 1 0 1
1 1 0 1 1 1
1 0 1 1 1 0 1
1 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0 1
1 1 0 1 1 1 0 1 1 1
1 0 1 1 1 0 1 1 1 0 1
1 1 1 1 0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0 1 1 1 0 1
(End)

Mathematica

rule = 188; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]

Crossrefs

Cf. A118173, A118174.

Sequence in context: A290228 A284029 A284408 * A284480 A290660 A292688

Adjacent sequences: A265424 A265425 A265426 * A265428 A265429 A265430

Keyword

nonn,easy

Author

Robert Price, Dec 08 2015

Status

approved