A266979 Binary representation of the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 101, 1111010, 10101, 11111101010, 1010101, 111111110101010, 101010101, 1111111111010101010, 10101010101, 11111111111101010101010, 1010101010101, 111111111111110101010101010, 101010101010101, 1111111111111111010101010101010, 10101010101010101

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 08 2016 and Apr 18 2019: (Start)

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

G.f.: (1+110*x-10000*x^2-100*x^3-100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=79; 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. A266978, A266980.

Sequence in context: A171797 A281173 A281219 * A267138 A039724 A008944

Adjacent sequences: A266976 A266977 A266978 * A266980 A266981 A266982

Keyword

nonn,easy

Author

Robert Price, Jan 07 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