A267057 Binary representation of the n-th iteration of the "Rule 97" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 10100, 10011, 100000000, 11111111, 1010000000000, 1001111111111, 10000000000000000, 1111111111111111, 101000000000000000000, 100111111111111111111, 1000000000000000000000000, 111111111111111111111111, 10100000000000000000000000000

Offset

0,3

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) = a(n-2)+100000000*a(n-4)-100000000*a(n-6) for n>5.

G.f.: (1+10099*x^2+10011*x^3-10100*x^4+11101100*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1+10000*x^2)).

(End)

Mathematica

rule=97; 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. A267056, A267058.

Sequence in context: A083965 A161022 A293686 * A213182 A213184 A267645

Adjacent sequences: A267054 A267055 A267056 * A267058 A267059 A267060

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