A267153 Binary representation of the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 1011, 1101110, 1110111, 11110111010, 111011011, 111111011111110, 11100000111, 1111111101011111010, 1101100011011, 11111111111111011111110, 11100000111, 111111111111111101011111010, 1101100011011, 1111111111111111111111011111110, 11100000111

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 11 2016 and Apr 19 2019: (Start)

a(n) = 10000*a(n-2)+a(n-4)-10000*a(n-6) for n>12.

G.f.: (1 +100*x -8989*x^2 +101110*x^3 -8999890*x^4 +99010910*x^5 -10990090000*x^6 +9900910000*x^7 -1099001110000*x^8 +989801000000*x^9 -109887911000000*x^10 +100990000000000*x^11 -11009890000000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +x^2)).

(End)

Mathematica

rule=107; 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. A267152, A267154.

Sequence in context: A266838 A267127 A266893 * A343294 A025421 A300254

Adjacent sequences: A267150 A267151 A267152 * A267154 A267155 A267156

Keyword

nonn,easy

Author

Robert Price, Jan 11 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