A267206 Binary representation of the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 11111, 100010, 111010111, 1011111010, 1111100011111, 10001010100010, 11101011111010111, 101111100011111010, 111110001010100011111, 1000101011111010100010, 1110101111100011111010111, 10111110001010100011111010, 11111000101011111010100011111

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 +20*x +11311*x^2 +212120*x^3 +13121310*x^4 +131213100*x^5 +1212121000*x^6 +1121100000*x^7 +100000000*x^8 -111000000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +x^2)*(1 +10*x +100*x^2)*(1 +10000*x^2)). - Colin Barker, Jan 13 2016 and Apr 19 2019

Mathematica

rule=109; 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. A243566.

Sequence in context: A138118 A267130 A267850 * A091253 A267887 A151582

Adjacent sequences: A267203 A267204 A267205 * A267207 A267208 A267209

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved