A266718 Decimal representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 6, 123, 12, 2039, 24, 32751, 48, 524255, 96, 8388543, 192, 134217599, 384, 2147483391, 768, 34359737855, 1536, 549755812863, 3072, 8796093020159, 6144, 140737488351231, 12288, 2251799813677055, 24576, 36028797018947583, 49152, 576460752303390719, 98304

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 04 2016 and Apr 18 2019: (Start)

a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>6.

G.f.: (1-2*x)*(1+7*x+x^2+30*x^3+8*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).

(End)

Mathematica

rule=59; 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. A266716, A266717.

Sequence in context: A041139 A065354 A078984 * A041257 A337465 A041411

Adjacent sequences: A266715 A266716 A266717 * A266719 A266720 A266721

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022

Status

approved