A266975 Binary representation of the n-th iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 11100, 1101000, 111010000, 11010100000, 1110101000000, 110101010000000, 11101010100000000, 1101010101000000000, 111010101010000000000, 11010101010100000000000, 1110101010101000000000000, 110101010101010000000000000, 11101010101010100000000000000

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 08 2016 and Apr 18 2019: (Start)

a(n) = 2^(n-2)*5^(n-1)*(9*(-10)^n+2189*10^n-20)/99 for n>0.

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

G.f.: (1+100*x-10000*x^3) / ((1-10*x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=78; 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. A266974, A266976.

Sequence in context: A267577 A262779 A058935 * A265320 A109241 A090490

Adjacent sequences: A266972 A266973 A266974 * A266976 A266977 A266978

Keyword

nonn,easy

Author

Robert Price, Jan 07 2016

Status

approved