A267273 Binary representation of the n-th iteration of the "Rule 117" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 11000, 11111, 110000000, 111111111, 1100000000000, 1111111111111, 11000000000000000, 11111111111111111, 110000000000000000000, 111111111111111111111, 1100000000000000000000000, 1111111111111111111111111, 11000000000000000000000000000

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 14 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.

G.f.: (1+11*x+999*x^2-98900*x^3-1000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

a(n) = A266983(n), n>1. - R. J. Mathar, Jan 17 2016

Mathematica

rule=117; 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. A267272, A267274.

Sequence in context: A083442 A114120 A118557 * A138713 A267923 A068223

Adjacent sequences: A267270 A267271 A267272 * A267274 A267275 A267276

Keyword

nonn

Author

Robert Price, Jan 12 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