A267054 Binary representation of the n-th iteration of the "Rule 93" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 10100, 101111, 101010000, 1010111111, 1010101000000, 10101011111111, 10101010100000000, 101010101111111111, 101010101010000000000, 1010101010111111111111, 1010101010101000000000000, 10101010101011111111111111, 10101010101010100000000000000

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 10 2016 and Apr 19 2019: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.

G.f.: (1+11*x-x^2-10000*x^3-100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=93; 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. A267053, A267055.

Sequence in context: A204574 A267801 A050647 * A082265 A161761 A114754

Adjacent sequences: A267051 A267052 A267053 * A267055 A267056 A267057

Keyword

nonn,easy

Author

Robert Price, Jan 09 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