A266844 Binary representation of the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 10100, 1101000, 101010000, 11010100000, 1010101000000, 110101010000000, 10101010100000000, 1101010101000000000, 101010101010000000000, 11010101010100000000000, 1010101010101000000000000, 110101010101010000000000000, 10101010101010100000000000000

Offset

0,2

Comments

Rule 198 also generates this sequence.

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)*(-9*(-50)^n-2*5^n+209*50^n))/99.

a(n) = 10*a(n-1)+10000*a(n-2)-100000*a(n-3) for n>2.

G.f.: (1+100*x-1000*x^2) / ((1-10*x)*(1-100*x)*(1+100*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]]], {k, 1, rows}]   (* Binary Representation of Rows *)

Crossrefs

Cf. A266843, A266846.

Sequence in context: A063751 A266179 A163664 * A265319 A267854 A135645

Adjacent sequences: A266841 A266842 A266843 * A266845 A266846 A266847

Keyword

nonn,easy

Author

Robert Price, Jan 04 2016

Status

approved