A266983 Binary representation of the n-th iteration of the "Rule 81" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 11000, 11111, 110000000, 111111111, 1100000000000, 1111111111111, 11000000000000000, 11111111111111111, 110000000000000000000, 111111111111111111111, 1100000000000000000000000, 1111111111111111111111111, 11000000000000000000000000000

Offset

0,3

Comments

Rule 113 also generates this sequence.

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 08 2016 and Apr 17 2019: (Start)

a(n) = (49*(-100)^n + 5*(-1)^n + 2^(2*n+1)*25^(n+1)-5)/90 for n > 0.

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

G.f.: (1 + x + 999*x^2 + 1110*x^3 - 1000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=81; 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. A266982, A266984.

Sequence in context: A252039 A252033 A352751 * A227865 A267777 A034712

Adjacent sequences: A266980 A266981 A266982 * A266984 A266985 A266986

Keyword

nonn,easy

Author

Robert Price, Jan 07 2016

Status

approved