A266842 Decimal representation of the n-th iteration of the "Rule 69" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 20, 43, 336, 687, 5440, 10943, 87296, 174847, 1397760, 2796543, 22368256, 44740607, 357908480, 715833343, 5726601216, 11453267967, 91625881600, 183252025343, 1466015154176, 2932031356927, 23456246661120, 46912497516543, 375299963355136, 750599943487487

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 05 2016 and Apr 18 2019: (Start)

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

G.f.: (1+2*x-x^2+x^3-48*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=69; 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. A266840, A266841.

Sequence in context: A357485 A194999 A280436 * A254542 A202602 A097652

Adjacent sequences: A266839 A266840 A266841 * A266843 A266844 A266845

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved