A266846 Decimal representation of the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 20, 104, 336, 1696, 5440, 27264, 87296, 436736, 1397760, 6989824, 22368256, 111845376, 357908480, 1789558784, 5726601216, 28633071616, 91625881600, 458129670144, 1466015154176, 7330076819456, 23456246661120, 117281237499904, 375299963355136

Offset

0,2

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 05 2016 and Apr 18 2019: (Start)

a(n) = 2^(n-1)*(-(-2)^n+9*2^n-2)/3 = 2^(n-1)*A061547(n+3).

a(n) = 2*a(n-1)+16*a(n-2)-32*a(n-3) for n>2.

G.f.: (1+4*x-8*x^2) / ((1-2*x)*(1-4*x)*(1+4*x)).

(End)

Mathematica

rule=70; 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. A266843, A266844.

Sequence in context: A200538 A238118 A211953 * A207819 A297974 A280187

Adjacent sequences: A266843 A266844 A266845 * A266847 A266848 A266849

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved