A266872 Binary representation of the n-th iteration of the "Rule 77" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 10101, 101010, 101010101, 1010101010, 1010101010101, 10101010101010, 10101010101010101, 101010101010101010, 101010101010101010101, 1010101010101010101010, 1010101010101010101010101, 10101010101010101010101010, 10101010101010101010101010101

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 05 2016 and Apr 18 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

G.f.: (1+10*x)*(1+100*x^2) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=77; 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. A266873.

Sequence in context: A267677 A101305 A001098 * A267705 A086164 A138119

Adjacent sequences: A266869 A266870 A266871 * A266873 A266874 A266875

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved