A267127 Binary representation of the n-th iteration of the "Rule 99" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 1010, 1101001, 1100100, 11101010011, 1101001000, 111101100100111, 1101010010000, 1111101101001001111, 1101100100100000, 11111101101010010011111, 1101101001001000000, 111111101101100100100111111, 1101101010010010000000, 1111111101101101001001001111111

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

Empirical g.f.: (1 +100*x -10001*x^2 -1099*x^3 -10000*x^5 -899991000*x^6 +10000000*x^7 +10911000000*x^8 -20000000000*x^10) / ((1 -x)*(1 +x)*(1 -10*x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)*(1 +10*x +100*x^2)*(1 -1000*x^2)). - Colin Barker, Jan 11 2016 and Apr 19 2019

Mathematica

rule=99; 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. A267126.

Sequence in context: A379268 A001737 A266838 * A266893 A267153 A343294

Adjacent sequences: A267124 A267125 A267126 * A267128 A267129 A267130

Keyword

nonn,easy

Author

Robert Price, Jan 10 2016

Status

approved