A267599 Binary representation of the n-th iteration of the "Rule 177" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 1001, 101001, 10101001, 1010101001, 101010101001, 10101010101001, 1010101010101001, 101010101010101001, 10101010101010101001, 1010101010101010101001, 101010101010101010101001, 10101010101010101010101001, 1010101010101010101010101001

Offset

0,3

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

Conjectures from Colin Barker, Jan 18 2016 and Apr 20 2019: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>2.

G.f.: (1-100*x+1000*x^2) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=177; 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. A267598, A083584.

Sequence in context: A218640 A221347 A109431 * A140927 A261544 A097659

Adjacent sequences: A267596 A267597 A267598 * A267600 A267601 A267602

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Status

approved