A267041 Binary representation of the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 1010, 1100011, 1111100, 11110001111, 111110000, 111111000111111, 11111000000, 1111111100011111111, 1111100000000, 11111111110001111111111, 111110000000000, 111111111111000111111111111, 11111000000000000, 1111111111111100011111111111111

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: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>8.

G.f.: (1 +101*x-9091*x^2 +79810*x^3 -8080810*x^4 +100810100*x^5 -10092910100*x^6 -101000000*x^7 +10101000000*x^8) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).

(End)

Mathematica

rule=91; 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. A267015, A267042.

Sequence in context: A115826 A115775 A115800 * A290193 A289462 A289578

Adjacent sequences: A267038 A267039 A267040 * A267042 A267043 A267044

Keyword

nonn

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