A266984 Decimal representation of the n-th iteration of the "Rule 81" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 24, 31, 384, 511, 6144, 8191, 98304, 131071, 1572864, 2097151, 25165824, 33554431, 402653184, 536870911, 6442450944, 8589934591, 103079215104, 137438953471, 1649267441664, 2199023255551, 26388279066624, 35184372088831, 422212465065984, 562949953421311

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 08 2016 and Apr 17 2019: (Start)

a(n) = ((-4)^n+(-1)^n-1)/2+4^n for n>0.

a(n) = 17*a(n-2)-16*a(n-4) for n>4.

G.f.: (1+2*x)*(1-x+9*x^2-4*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

Crossrefs

Cf. A266982, A266983.

Sequence in context: A167307 A161378 A206448 * A217158 A214227 A337055

Adjacent sequences: A266981 A266982 A266983 * A266985 A266986 A266987

Keyword

nonn,easy

Author

Robert Price, Jan 07 2016

Status

approved