A267036 Decimal representation of the n-th iteration of the "Rule 85" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 16, 63, 256, 1023, 4096, 16383, 65536, 262143, 1048576, 4194303, 16777216, 67108863, 268435456, 1073741823, 4294967296, 17179869183, 68719476736, 274877906943, 1099511627776, 4398046511103, 17592186044416, 70368744177663, 281474976710656

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 11 2016 and Apr 19 2019: (Start)

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

a(n) = 4*a(n-1)+a(n-2)-4*a(n-3) for n>2.

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

(End)

Mathematica

rule=85; 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. A267034, A267035.

Sequence in context: A370305 A355645 A323941 * A037451 A247363 A007143

Adjacent sequences: A267033 A267034 A267035 * A267037 A267038 A267039

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved