A267293 Binary representation of the n-th iteration of the "Rule 121" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 11010, 111011, 111011100, 1011101111, 1101101110000, 11111110111111, 11100000111000000, 101111101011111111, 110110001101100000000, 1111111011111111111111, 1110000011100000000000000, 10111110101111111111111111, 11011000110110000000000000000

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 15 2016 and Apr 19 2019: (Start)

a(n) = a(n-2)+100000000*a(n-4)-100000000*a(n-6) for n>12.

G.f.: (1 +x +11009*x^2 +111010*x^3 +11000090*x^4 +910990100*x^5 +90098900*x^6 +9099010000*x^7 -1109990110000*x^8 +979901000000*x^9 -108789011000000*x^10 -989900000000*x^11 +109898900000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +10000*x^2)).

(End)

Mathematica

rule=121; 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. A267292.

Sequence in context: A045152 A251873 A267038 * A300557 A181319 A267811

Adjacent sequences: A267290 A267291 A267292 * A267294 A267295 A267296

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved