A266670 Binary representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 1000, 1011111, 1000000, 11011111111, 1000000000, 111011111111111, 1000000000000, 1111011111111111111, 1000000000000000, 11111011111111111111111, 1000000000000000000, 111111011111111111111111111, 1000000000000000000000, 1111111011111111111111111111111

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

Formula

Conjectures from Colin Barker, Jan 03 2016 and Apr 16 2019: (Start)

a(n) = 11001*a(n-2) - 10011000*a(n-4) + 10000000*a(n-6) for n>5.

G.f.: (1+11*x-10001*x^2+890100*x^3+10000*x^4-2000000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).

(End)

Mathematica

rule=53; 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. A266669, A266671.

Sequence in context: A281628 A278955 A278753 * A272654 A342036 A004656

Adjacent sequences: A266667 A266668 A266669 * A266671 A266672 A266673

Keyword

nonn,easy

Author

Robert Price, Jan 02 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022

Status

approved