A263244 Binary representation of the n-th iteration of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 10011, 1011111, 100111111, 10111111111, 1001111111111, 101111111111111, 10011111111111111, 1011111111111111111, 100111111111111111111, 10111111111111111111111, 1001111111111111111111111, 101111111111111111111111111, 10011111111111111111111111111

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 20 2016 and Apr 17 2019: (Start)

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

G.f.: (1+100*x-90*x^2+1100*x^3) / ((1-x)*(1-100*x)*(1+100*x)).

(End)

Conjecture: a(n) = floor(91*100^((n-1)/2)*10^n/9) for odd n; a(n) = floor(901*100^(n/2 - 1)*10^n/9) for even n. - Karl V. Keller, Jr., May 01 2022

Mathematica

rule=155; 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. A263243, A263245.

Sequence in context: A262861 A371563 A164367 * A368417 A094028 A144564

Adjacent sequences: A263241 A263242 A263243 * A263245 A263246 A263247

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved