A267254 Binary representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 111, 1111010, 11111, 11111100010, 1011111, 111111111100010, 1011111, 1111111111111100010, 1011111, 11111111111111111100010, 1011111, 111111111111111111111100010, 1011111, 1111111111111111111111111100010, 1011111, 11111111111111111111111111111100010

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

Formula

From Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>8.

G.f.: (1 +110*x -9890*x^2 +10900*x^3 -1089000*x^4 +989000*x^5 -109000000*x^6 +110000000*x^7 -10000000000*x^8) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).

(End)

a(n) = floor(10*100^n/9) - 11101 for odd n>4; a(n) = 1011111 for even n>4. - Karl V. Keller, Jr., Sep 14 2021

Mathematica

rule=111; 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 *)

Prog

(Python) print([1, 110, 111, 1111010, 11111] + [10*100**n//9 - 11101 if n%2 else 1011111 for n in range(5, 50)]) # Karl V. Keller, Jr., Sep 14 2021

Crossrefs

Cf. A267253, A267255.

Sequence in context: A288769 A112891 A182621 * A036230 A171236 A279421

Adjacent sequences: A267251 A267252 A267253 * A267255 A267256 A267257

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved