A267677 Binary representation of the n-th iteration of the "Rule 197" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 10100, 1101000, 111010100, 11110101000, 1111101010100, 111111010101000, 11111110101010100, 1111111101010101000, 111111111010101010100, 11111111110101010101000, 1111111111101010101010100, 111111111111010101010101000, 11111111111110101010101010100

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 and Apr 20 2019: (Start)

a(n) = 110*a(n-1)-999*a(n-2)-110*a(n-3)+1000*a(n-4) for n>5.

G.f.: (1-100*x+9999*x^2+100*x^3-9900*x^4-10000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).

(End)

Mathematica

rule=197; 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. A267676, A267678.

Sequence in context: A119037 A327232 A266841 * A101305 A001098 A266872

Adjacent sequences: A267674 A267675 A267676 * A267678 A267679 A267680

Keyword

nonn,easy

Author

Robert Price, Jan 19 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved