A266752 Binary representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 10010, 1001010, 100101010, 10010101010, 1001010101010, 100101010101010, 10010101010101010, 1001010101010101010, 100101010101010101010, 10010101010101010101010, 1001010101010101010101010, 100101010101010101010101010, 10010101010101010101010101010

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

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

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

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

(End)

Mathematica

rule=163; 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. A263919, A266753.

Sequence in context: A045799 A096885 A267449 * A267523 A027576 A099374

Adjacent sequences: A266749 A266750 A266751 * A266753 A266754 A266755

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved